Solving 'impossible' integrals in seconds

[@yashwanthracha7991]

Jee main is not entrance exam for IITs it's only eligibility test to write jee advanced which is the gruesome one which will give admission in IIT

[@HritikRoshan-uk5py]

Only a jee aspirant can realise it much better

[@universeboss1]

Right!

[@addityasinghal897]

That's what he said. "It is a precursor to the exam to get into IIT", which is the advanced set

[@anishsaju7211]

Bro what he said is correct.before 2012. Jee advanced was named IIT JEE.and JEE main as AIEEE.the problem is very old JEE advanced problem.the very old JEE ADVANCED problems can be found in ncert maths text book.

[@hiwakraulkar2635]

@@anishsaju7211 Correct Bro,☑️☑️☑️☑️☑️☑️

[@Robi2009]

Solve in seconds... as long as you know some obscure integral formula for substitution... If you don't know this formula, you're screwed. Yup, great challenge.

[@evlredsun]

different places teach different obscure integral formulas depending on the program, some common integral formulas are more useful in different scenarios. for example, i take economics, so they never teach trigonometric identities because we never use them, whereas they are essential for most of physics. certain types of physics rarely use e, whereas economics uses it constantly. pun intended.

[@samruddhisaoji7195]

Even without the formula, it takes like 30 sec to solve

[@samwong9489]

actually, let u = a+b-x ,then its new definite intergral will always equal to the orginal one, you should memorise the proof itnstead of the stpuid formula which may be some simpified version for exam purpose only

[@twwilight_gaming3172]

Its a common technique and is taught by the name of “king’s rule” all over india. Different places have different different formulas for simplifying integration but its scattered all over the world. No one has a complete knowledge of integration

[@possessedchair8144]

@@evlredsun There's virtually no area of physics that doesn't make extensive use of the constant "e".

[@arvindkumar-gp2ol]

Plzz don't shame JEE main, this is the easiest question of definite integral...from NCERT class Xll part -2....

[@anilkumarshukla9107]

Yes.....we have these type of integral problem for 6 marks in our 12th pre board exams

[@alkanedust3848]

r/iamverysmart

[@multilogic2746]

And he is saying JEE MAINS entrance exam for IITs somebody please tell him about JEE ADVANCED

[@1_adityasingh]

@@multilogic2746 He said that it's a precursor to the exam to get admission into IIT.

[@manansheth3084]

Ya I haven't learnt any math after my 3rd sem which was 4yr ago still I solved it😅 just took some time to recognize the pattern of question and then it was done.

[@xyZ-st9ry]

Le JEE Advanced - this isn't even my final form

[@simarpreetsingh7235]

Jee advance: i used to solve these in XI physics

[@piyushpandey3935]

This is JEE Maine not JEE Advanced

[@jyotsnasrivastava6373]

Its not that dificult if you take some tutorial class which is a must. He didnt mentioned the rule that in definite integration, integral(a to b f(x))=integral(a to b f(a+b-x)). This rule is used to derive above expression. And this is a very basic rule even taught in schools in class 12 and its very normal

[@Idontcare-qy9yb]

@@jyotsnasrivastava6373 exactly

[@Idontcare-qy9yb]

@@jyotsnasrivastava6373 are you jee aspirant

[@OAayu]

That's not a level of jee main. It's a board base questions. ...

[@nitd955]

Not even board

[@adveshdarvekar7733]

These kinds of questions do come in jee mains.

[@Idontcare-qy9yb]

@@adveshdarvekar7733 rarely

[@randomhooman3236]

@@adveshdarvekar7733 these types of ques used to come when JEE main was conducted by CBSE now it is conducted by NTA and those questions are tough

[@simran8109]

True😂😂

[@igoryegin9531]

Here's how to solve this within seconds Step 1. Be born in India

[@jarvischristiron779]

Lmao🤣🤣🤣!!

[@xXmayank.kumarXx]

How to solve this within milliseconds Step 1: Be born in China 🙂

[@sonalibbhuyan921]

You will regret it

[@sharathgowtham2157]

Corona virus bruh

[@moumitamajumdar7116]

Step 2. Take medical😂😂

[@soumyadeepvishwakarma3875]

For those who are confused at 5:18 why did the limits changed? When we change the variables (i.e. from x to u) we also have to change variables i.e. upper limit for x is b but we're substituting u=a+b-x so when we put x=b in u=a+b-x it becomes u=a+b-b so b cancels out and upper limit converts to a and in same way x=a in lower limit converts to b

[@yashmehta830]

he subsituted u=a+b-x so if you calculate value of u when x=a then u = a+b-a= b and similiarly when x=b then u will be a, hence the limits of integral changes

[@soumyadeepvishwakarma3875]

@@yashmehta830 exactly 👍

[@rithroeurn1719]

Thank🥺

[@siddharthannandhakumar6187]

My doubt is, initially he substituted u=a+b-x, but later he simply substituted x for u... Shouldn't that be x=a+b-u?

[@learnsciencewithinaaya1405]

@@siddharthannandhakumar6187 u is a dummy variable. You can refer following property of definite integral Integration. limit a to b f(x)dx = limit a to b f(t)dt

[@angrytedtalks]

When I come across an integral like these (as a taxi driver) I promise I shall use this technique. 😳

[@greenwaldian]

😂😂😂

[@ionut.666]

that's why you are a taxi driver!

[@angrytedtalks]

@@ionut.666 Taxi driver is my day job. By night I am a business consultant, philosopher, educator and entertainer; not much need for this type of equation in any of those fields. Actually, the vast majority of occupations have no need for this technique, but it is good to know.

[@toasterr4238]

@pola os doubt you have any to give out.

[@lecinquiemeroimage]

Ted, you don't need to know this "useless" formula ! For example let's call I = ∫₀ₐ √(sinx) dx/[√(sinx) + √(cosx)] and J = ∫₀ₐ√(cosx) dx/[√(sinx) + √(cosx)] (please note that a = π/2 → π/2 is very difficult to write inside the integral). Then we have I + J = ∫₀ₐ1.dx = [x]₀ₐ = a - 0 = a = π/2 Now let's show that J = I : as we know sin(π/2 - t) = cost, and cos (π/2 - t) = sint, then we are led to note x = (π/2 - t) ⇒ dx = - dt and J = ∫ₐ₀√(cos(π/2 - t).(-dt)/[√(cost) + √(sint)] = ∫₀ₐ√(sint).dt/[√sint + √cost] = I The end : I + J = π/2 ⇒ 2I = π/2 so I = π/4. To serve you. professor essef, in mathematics (active on YT and Wiki, in astronomy and astrophysics). Paris, Saturday, May, 23, 2020.

[@muonline2067]

in many Asian countries, Viet Nam, Korea, Chinese, all the high school pupils learn how to solve this problem. The only problem is that this kind of math can not help them to be a good student in the future. I had learned all of them 20 years ago, and I never use them again. even so far I am a Ph.D. in computer science in Germany. Therefore, I do not waste your time on them, except in case you should solve them for the exam in order to get a slot in Uni.

[@1tubax]

Speed is not king in the real life. It's always a slow, strategic methodical grind. Even in sports and gaming where speed is indeed very important, you have to grind your base strengths and practice and develop advanced strategies. Getting faster and faster for the purpose of getting faster will lead you absolutely nowhere.

[@enejidjsi5939]

@@1tubax unfortunately our indian government doesn't understand this. Jee mains focusses a lot more on speed and accuracy rather than testing actual concepts. I guess it had to be this way because of the high population here, so they could sort through talent quickly :(

[@1tubax]

@@enejidjsi5939 it's also a poor way of picking talent. Just because you are fast doesn't mean you're creative or innovative or can understand concepts well. Can elon musk succeed in a jee exam? Nope, but he can solve many problems people can't.

[@enejidjsi5939]

@@1tubax right, it's unfortunate me and millions of others have to slave away grinding problems just to get selected in IIT, and not for the sake of learning. I wish I didn't have to do this, but it's the only choice.

[@1tubax]

@@enejidjsi5939 self study igcse and a levels online and take the exams. They're a bit pricy for the average salary but they get you much farther than standard indian curriculums

[@PaulMurrayCanberra]

Visually, f(a + b - x) is the horizontal mirror image of f(x) over the interval (a;b).

[@mdshawonprodhan1154]

Yes.....

[@ankitkant]

It is a class 12 level integral... And from NCERT

[@devleena7990]

Yeah the problem 8n the thumbnail is in ncert ch:7- ex:7.11, Pg 347 😉

[@manolgeorgiev9664]

And then there's people like me, who haven't learned integrals in school at all.

[@douglasbrinkman5937]

just last week, while in line at the bank, a guy said "solve this equation and I won't shoot you" phew. that was close.

[@willymegakek7637]

i know right, people in the neighbourhood arent even going to rob me anymore since they know i have proper integration techniques

[@menma2914]

Why do you watch educational videos when you think they have no meaning in your life?

[@RenegadeRacoon]

Modern days' clown of the class be like

[@bait5257]

@@RenegadeRacoon 😂

[@tseringchosphel1340]

@ཏྦཱལ་ག་པོ། you have tibetan script name

[@pluto8404]

This is piece of cake for those that took math 3000: insane integration When I doubt, put horseshoe.

[@Dr.farazalam]

If you go read the NCERT textbook, it is a simple method in Definite integrals. .. byjus.com/class-12-maths-ncert-book/ chapter 7 integrals

[@psibarpsi]

@@Dr.farazalam you clearly don't know what a joke is.

[@Dr.farazalam]

@@psibarpsi this question is really a very easy one.. Might come as a one marker

[@psibarpsi]

@@Dr.farazalam I know, genius. And that was NOT what I was pointing at.

[@jflores8914]

@@Dr.farazalam j

[@sohanbhattacharyya8451]

Ik this turned out to be too long, bt give it a read, it's really helpful to those who were not taught this property, and even for those who know this property since I got over slightly on the intuition behind it. There's a common property of definite integration we are taught here in India integral from a to b of f(x)=integral from a to b of f(a+b-x) You can prove this by putting u=a+b-x, in a manner similar to how he proved this case. This problem he showed is a special type, where everything just cancels off. But i wanna say why this works, like not the mathematical proof, bt a more intuitive one. The integral from a to b of f(a+b-x) is actually nothing bt evaluating the original integral just in a backward direction (from b to a) When you're at a, the differential is f(a+b-a)dx=f(b)dx When you reach b, the differential is f(a)dx. Summing up all the small strips of area, we get the same thing, the area under the curve of f(x) from a to b. This was the intuition behind this "King's property" (that's what we call it here) This property can be used in almost every question of definite integral to make the final integrand super easy. To use this directly, When I=integral from a to b of f(x), After applying this property, I=1/2(integral from a to b of [f(x)+f(a+b-x)]dx) In India, we're not really taught the actual intuition behind it (most teachers don't), bt I think it's good to know this.

[@sincosfunnpe6671]

😲 thank you. did not know what it actually did

[@julianbruns7459]

Thanks for the explanation. Are there any similar tricks that you could share?

[@arunyesare5959]

Always answer is →π/4 .This question can be asked in 11 types

[@vasu-fu9cb]

How sir

[@MBA_Farmer]

Absolutely sir

[@Johnny.Fedora]

That's funny. In the U.S. medical school STEP test, if one of the answers to a question is "hepatitis," then the correct answer to the question is "hepatitis."

[@icrazytheorist9114]

Really appreciate the fact that you put on questions from our competitive exams, your channel really grows to be diverse in questions from all over the world, while questions from our exams seem pretty easy, questions from other countries are often tough and sometimes impossible! Thanks for making an archive of all the questions:) Love from your fans!

[@CooperRussell5]

Teachers hate him, Watch how he solves complex problems in seconds with this one trick!

[@himanshuchougule471]

Haha

[@KrBme78]

He's given a complicated integral. What happens next will ASTOUND you!

[@dekz0911]

LoL complex xD

[@ianmi4i727]

I'm a math teacher and I Love it!! :D

[@fourtoedhedgehog9412]

with this one WIERD trick

[@srishtikdutta8946]

This is very old IIT JEE problems, which are a piece of cake. Recent Problems are much better.

[@aryankhullar7101]

@shashwat gupta nope thats not true, it was a fairly tough paper compared to previous ones

[@aryankhullar7101]

@shashwat gupta ohk, btw are u a jee aspirant or in college

[@aryankhullar7101]

@shashwat gupta same which coaching do you go too?

[@aryankhullar7101]

@shashwat gupta i am currently studying in vidyamindir classes, is gravity in kota?

[@aryankhullar7101]

@shashwat gupta you go both fiitjee and gravity or u use dlp program with fiitjee

[@adityaranjansahoo6261]

its the BASIC QUESTION OF KING'S PROPERTY: LIMITS A To B wrt fx can be resolved as limits from a to b with Integrating f(a+b-x) wrt dx

[@adveshdarvekar7733]

This video means so much to me. I'm an Indian preparing for iit jee. Its so tough. Thank you for making it so easy

[@ishaangulia7241]

How did your advance go

[@Amit_Pirate]

Hi, how did your advanced go

[@vadirajkulai3736]

Trust me.. I've given these exams... The question you've given in the video is one of the easiest ones... It's a freaking tough exam. Please do more videos on IITJEE problems... Love your channel ✌️

[@AmanKumar-vd1jc]

@@anandk9220 answer to second question is (4 -3√2)/4

[@AmanKumar-vd1jc]

@@anandk9220 answer of question1 is 3/2(e^5/2)

[@anandk9220]

@@AmanKumar-vd1jc Are you IITian or IIT aspirant?

[@anandk9220]

@@AmanKumar-vd1jc As far as I can recall, I have never ever learnt this property (used in question 1) in my class 12 math ∫ [ f(x) + x f'(x) ] dx = x f(x) + c Perhaps this property is studied and included primarily in JEE Math. I've not studied or appeared for JEE so I didn't have any idea about this.

[@AmanKumar-vd1jc]

@@anandk9220 preparing for IIT

[@jessstuart7495]

That is one of the coolest integration tricks I've ever seen. Thanks!

[@AmarKumar-zf7vk]

This is my board questions lol😂

[@ashutoshsanghi9681]

Shi me bhai last exercise ka h ye ,inhe to ye simple integral ke liye bhi direct formula yaad krte h😂😂

[@maazansari8660]

NCERT KA H😂😂

[@KING-ni4ze]

ICSE board hai na tera? 😂

[@thedoctorunofficial]

I hope you used the proof based method to solve rather than applying the formula.

[@youtubeshortsviral1361]

Help me, 5:27 me "u" ko direct "X" Mai kaise convert kiya

[@ChidVanhi]

I took 1.5 minutes for solving all 3 now. I was much faster when I was giving my Maths exam in XII.

[@Anonymous-jn3rs]

We'll recommend for Nobel prize for saving the humanity..

[@gurnoorsingh4396]

@@Anonymous-jn3rs true. We indians suffer from a huge superiority complex over others.

[@Ambigious]

@@gurnoorsingh4396 We can tell Yet the actual economy has little to show for it

[@Ankit-cs8un]

@@gurnoorsingh4396 so true

[@nikhilnagaria2672]

ok flexer

[@alirezapouladkhan7291]

I really enjoyed this formula, it's amazing!

[@abromchris7670]

Thank you, dude. Your pronounciation is really clear. Taiwan student. (￣▽￣) this really saves time.

[@snehpatel60]

@@sanyamjain7058 Bro you've said this on every comment....

[@harshitgupta7496]

These are very easy questions to be in India JEE exams!! In India class 12 every one knows about these tricks . Presh talwalkar can you please make a video on one of the paradox (I need it for my maths project) pls?

[@potato5848]

a and b are two numbers having the same no. of digits and same sum of digits (=28). Can one be a multiple of the other? a is not equal to b. This question is asked in 2019 interview of Indian statistical Institute.

[@ianmaateus]

It is not possible for one to be multiple of the other. Imagine that a were equal to bm for some m natural. Because a and b have the same number of digits and are not equal, 1 < m < 10. As the sum of digits of a is 28, we know that a leaves remainder 1 when divided by 9. Similarly, b leaves remainder 1 when divided by 9. That being the case, 2b leaves remainder 2, 3b leaves remainder 3, ..., 8b leaves remainder 8, 9b leaves remainder 0 when divided by 9. So it is not possible for a to be any of the numbers 2b, 3b, ..., 8b, 9b. This reasoning shows that m cannot exist.

[@potato5848]

@@ianmaateus thank you so much sir😊😊

[@GrimReaper-gt2xs]

I Would say its a senseical problem rather then difficulty but here what i did to solve this is that i put a=a1.a2.a3..........an for a1,a2,a3,.....,an as digits of a and b=b1.b2.b3......bn for b1,b2,b3,b4,b5,.....,bn as digits of b as n on both as total digits of both are equal now here suppose ax=b for x an integer and 1

[@jongyon7192p]

oh it HAS to equal 28? I was just gonna mention 142857...

[@vishalmishra3046]

No. Here is why : 9+9+9=27 < 28, so both a and b are at least 4 digit numbers. Same number of digits implies a/b = single digit > 1 (since a not equal to b) - e.g. 7777 or 6688/3344. So, if sum of digits is fixed (28) and number of digits has to be same, then a has to be equal to b = 7,777 or 4,444,444.

[@jacobpierri5535]

A shorthand explanation of the above formula is this: Since sine and cosine are identical but backwards over the interval, the integral would be the same with sqrt(cosine) on top. If you add this new integral to the one with sine, you get the same numerator and denominator, meaning an integral of 1 over the interval of 0 to pi/2. Then you just divide by 2. If this doesn't make sense, it's because I don't have access to symbols!

[@ankitbhattacharjee_iitkgp]

JEE Main 2023 has come miles ahead of this type of questions which are solved using King's Rule. These questions would be way easier than the easiest question of JEE Main 2023. Even boards (for me WB board) now-a-days ask harder questions than these.

[@javastream5015]

The guy who found out this formula was smart. Bytheway, we in Switzerland never learned this formula. Even if it’s over 23 years ago, I don’t remember having seen it. Different education goals?

[@donaldbiden7927]

This is a trick used by many Indian students

[@57thorns]

I suspect different education system focus on different formulas to memorize. You can probably deduce most formulas you need, but it takes time. This is not to bad in real life, because you might need an hour or two to either figure it out, or look it up, in a project that takes months (if the end result is software) or years (if the end result is engineering). Getting it right is more important at this stage than being quick. Exams have a very limited time span, so they tend to rely on memorized formulas. After all, if you had it memorized once, you are likely to recognize it when you look it up. But there are too many formulas available, so only a small subset it taught. Some, like the formula for solving quadratic equations, seem to be universal, but when it comes to integrals, the shortcuts taught varies. Point in case: In a algebra exam at university, I had two complex logical expressions that I needed to prove equal. In real life, I would just set up a computer and run through all 1024 combinations (if there were 10 variables, and I believe there were even fewer). But this would be pointless. The idea here was that there was a lemma in the book that we were supposed to refer to which would solve this in seconds. Assuming you had spent either five minutes memorizing it (and it stuck), or a few hours with the proof (and not had time for everything else in the curriculum). Well, I did well on the test, I had two questions left with two hours to go. One question I had no idea here to start, but this one I brute force over three hand written A4 papers in the time I had left. The professor had to give me full points, because I had executed it flawlessly. So, which of these three approaches would have worked in real life? Memorizing without understanding, and the formula would be gone six months after the test. Learning the hard way, and it would hang around for years. This method? I can probably do it again because I only used basic techniques that I will remember as long as my brain is in half decent shape. But it would be hard and slow work. I will not win competitions, but if that software we are building depends on it at least i can be pretty sure I got this right.

[@rob6129]

These questions basically boil down to knowing the trick. But i still think have to revise my integral knowledge

[@collegestudent6071]

Same in America. Guess we'd rather prioritize understanding how to solve the problem rather than using tricks.

[@jamesdsa1965]

Mate, trust me, you guys are better off with the education techniques that you have in Switzerland. In India, it's all about doing these problems by learning tricks and that's about it! Who do we think about when we think of Quality, Precision, and standards? Switzerland! And I am telling you this as an Indian. Having personally studied abroad, I know that in foreign Universities, the emphasis is on learning it properly. Just the like the American guy wrote, the Universities that I have come across have emphasized on getting the basics right. When we think about Engineering, we think about the US, Europe, Japan, etc. And on top of that, India is plagued with the reservation criteria where a person's cast determines what would be his cut - off grades for entry into Governmental institutions. You ask anyone in India and they will speak highly of the IITs, the NITs, etc. But, despite having all these bright students, India is still plagued by failures. In 2019, a mission to Moon didn't go right. The Indians took solace in the fact that the big countries like US, Russia, themselves had to try more than 10 times, while conveniently forgetting that those attempts were made in the 50s and 60s. Indian education system is meant for culling the over - population from having bigger dreams. After all, they can't afford to have so many educated people. These tests are really hard. People prepare for years for them. Those who clear it, then take their legs off the pedal because they now think they deserve to enjoy the benefits of their personal hard work. Another thing in which Indians will take pride is in telling everyone how a majority of scientists and engineers in the US companies are Indians. They forget that you can't be Indian if you want to be working in these companies. They apply for the PR and the eventually give the test for citizenship. Citizenship! They pledge their allegiance to the US Flag. Now US is one country where people like to celebrate their dual nationality but India isn't. India clearly doesn't allow dual citizenship. And if at all they do provide it to these eminent people, it is just to earn brownie - points. Point is, everybody wants to go to the west because there is literally nothing happening here. Only thing you can set up are big software companies. Core mechanical is down in garbage. We have been trying to produce an indigenous Light - combat aircraft and its very own engine, since the past 30 - 40 years. Guess what, nothing has happened. Imagine, a country that has an engineering institution that requires people to give the above shown tests to get into, can't produce its own products. Now here's the last bit, I spoke to you as an Indian talking about openly about the short comings of my country. Given how KZbin displays my name. There will be people, from my own country, disagreeing with me (which is obvious) and going after me because I do not share the same religion, caste as them. So yeah, education in India is only about these equations. The moral values of being a human is absent.

[@Sorya-gf7qw]

In comment section all my brothers who went for coaching for IITs

[@abhigyagupta9499]

Students who gave this year's Mains be like, "If that should be Mains's level, I don't know which paper I gave!!"😂

[@manishkumarshakya7989]

😂😂 Easy tha is baar to Mai NEET aspirant hu mgr mujhe bhi easy lga tha 😂 Phy, Chem me

[@abhigyagupta9499]

@@manishkumarshakya7989 Physics and chem toh badhiya hi thha... Majority ki toh maths ne hi maari thhi😂😂 (Best of luck for NEET!)

[@Yoongiluvbot]

I hope this is class 12 and not 11 I’m already feeling worthless

[@aviralagarwal2369]

@@Yoongiluvbot yup 12th

[@Yoongiluvbot]

@@aviralagarwal2369 better

[@parthpandya6412]

Even in India this formula is generally not taught, instead they always teach us that integral of f(x) is equal to integral of f(a+b-x), these questions were made so that students apply the above rule. But vedantuJee just exploited the formula and made that new one.

Thank you so much. If only teachers teach like you did, in about 6 minutes...

[@bedo2445]

5:29 Don't understand why replace u with x isn't it equal to a+b-x?

[@codeRush]

Let x=a+b-x So taking derivatives both side u get dx=dx hence there is no harm replacing it . Only limits of integral changes.. Which actually leads us to proof of it.. I wish I could attach a pic of proof here. :(

[@fabiane6969]

The replaced x is indeed a different variable from the x in the first integral. But since you are integrating over these variables, the name of the variable of the integrand which goes from a to b is irrelevant, because it's just about what numbers the variable is running through and what values the integrand has for these numbers.

[@bedo2445]

@@codeRush I think you men dx = -dx

[@bedo2445]

Thanks all i get it now

[@codeRush]

@@bedo2445 yes

[@rickperry9457]

This has to be one of the best youtube channels out there for math.

[@nchoosekmath]

Such a beautiful theorem and beautiful proof too. I wonder for each problem, is there a way to solve them without using this trick? The first one, you definitely can do by conjunction. But for the rest, haha, seems hopeless.

[@leif1075]

What do you mean by conjunction??

[@hamiltonianpathondodecahed5236]

just like he proved the king's property, u can do it step by step see bprp video on king's property

[@nchoosekmath]

Leif conjugation I meant lol.

[@sharpnova2]

@@nchoosekmath again.. what the hell is conjugation..? I've only ever heard that in language

[@twwilight_gaming3172]

n choose k we in india are taught this trick in class 12

[@sahilbait2981]

I solved in 10 seconds 😂 famously known as king rule 🔥

[@rahulrajss723]

Exactly Even me too... I thought People saying my child is studying in Foreign means. He is a Intelligent. But, Wait. I solved before he even see this question.

[@ashitbhagat2510]

Same

[@bikramadityarajendrapatra3447]

What is king rule please explain

[@vroq2]

@@rahulrajss723 it's given in NCERT lmao

[@monty6108]

bohot time le liya bhai

[@dirkmcliesh]

You can do this without the general formula - just break it into two segments (0, PI/4) and (PI/4, PI/2) and then substitute in the second segment x' = PI/2 - x (and then replace again with x = x'), then recognise that sin(PI/2 - x) = cos(x) and vice versa, and then you'll see you have a single integral of unity [ { sqrt(sin(x)) + sqrt(cos(x)) } / { sqrt(sin(x)) + sqrt(cos(x)) } ] over the period (0, PI/4) which of course equals PI/4

[@aryandas6403]

All questions took me less than a minute to solve, very easy question picked up from mains, there are many difficult questions available.

[@xtehmoonlight7400]

How to solve this question in seconds First I was like, is there some interesting trigonometry identity trick to use? The answer is "use this formula"

[@samriddhisharma7779]

In india we can solve this by just looking at it.... And the sad part is we get more difficult trigo problems than this one in our exams and we have to use 2 to 3 tricks t to solve it...

[@adamdoni]

Why after subtitute the limit is flipped?

[@shmuelzehavi4940]

@@adamdoni The variable "u" is defined as: u = a + b - x Whenever you change the integrating variable, then you must change the limits to the values of the new integrating variable at the limit points. Then: x = a ⟹ u = a + b - a = b x = b ⟹ u = a + b - b = a I hope it answers your question.

[@Abhishek-kw9sp]

@@charmelonchannel Being an IITian (IIT Delhi, 2021 batch) I can tell you that what you're saying is wrong for so many reasons. Some of them are.. 1.) It's an exam for engineering entrance not for a mathematics UG program. So it focuses more on your problem solving skills rather than theoretical skills or in your case asking to prove stuff. And considering the exam's difficulty level and other situations they are not just testing your IQ but your EQ as well. 2.) It's like the most easiest problem in that exam but a lot of problems are of Olympiad difficulty level and a lot physics problems they gave are so twisted sometimes that they even change the fundamentals so that you have to derive the whole thing from the bottom. You gotta have your basic foundation strong to do so. 3.) And finally, FYI selection rate of this exam that you're talking about is around 0.33%, and selected students goes to the most Elite Colleges in our country. P.S. - I didn't mean any harm, just want you to realise that it's not a piece of cake to compete in millions to get a 3 digit rank PEACE ✌️

[@lecinquiemeroimage]

You don't need to know this "useless" formula ! For example let's call I = ∫₀ₐ √(sinx) dx/[√(sinx) + √(cosx)] and J = ∫₀ₐ√(cosx) dx/[√(sinx) + √(cosx)] (please note that a = π/2 → π/2 is very difficult to write inside the integral). Then we have I + J = ∫₀ₐ1.dx = [x]₀ₐ = a - 0 = a = π/2 Now let's show that J = I : as we know sin(π/2 - t) = cost, and cos (π/2 - t) = sint, then we are led to note x = (π/2 - t) ⇒ dx = - dt and J = ∫ₐ₀√(cos(π/2 - t).(-dt)/[√(cost) + √(sint)] = ∫₀ₐ√(sint).dt/[√sint + √cost] = I The end : I + J = π/2 ⇒ 2I = π/2 so I = π/4. To serve you. professor essef, in mathematics (active on YT and Wiki, in astronomy and astrophysics). Paris, Saturday, May, 23, 2020.

[@nisharathore8754]

Thumbnail pe jo problem thi vo to dekhte hi solve ho gayi thi properties se😁😁👌🏻👌🏻👌🏻👍👍😂😂

[@pwsk]

Good question Right explanation Brilliant teacher

[@shivam8809]

Your mind will blow out after seeing jee advance problem

[@atharvachaudhari6325]

One of the best trick I have seen in my life .... Those who are preparing for JEE Mains & Advanced MUST WATCH THIS VIDEO 😃😃 Thanks for making this video & helping us 🙏🙏

[@experimentbysaifanali7580]

What is Jee main and Jee advance??

[@shadowclan5859]

JEE Mains leads to admissions in NITs, second most prestigious institution in India, and gives the eligibiliy to write JEE Advanced Exam, which then gives admission in IITs.

[@mmattoso1]

I know this one since about 40 years ago, when I was taking the preparatory course for the admission exams for my university in Brazil... it actually works for any function of (sin) and (cos), does not need to be the square root... 😉

[@krishgarg2806]

PS: for someone curious, in definite integration, a->b f(x) dx, we can substitute x -> a+b-x and the integration value remains the same. This is known as the Kings Property, which is pretty common and should be known by anyone learning integration.

[@micearetrash]

1:34 from where i come we call it the starter formula because it literally starts every problem solving when you cant think of anything Just replace x with a+b-x and then add the new eq with the original eq

[@frostinfy169]

I'm Indian, therefore I solved the question before it even popped up...

[@HritikRoshan-uk5py]

Yeah, mains is relatively easy but jee advance questions requires time

[@siddharthsaxena7466]

Rip logic Dude you solve the question not answer

[@pxnishant]

hahaha

[@AdiBenIsrael]

What took you so long?

[@lecinquiemeroimage]

Are you so strong in physics, in India ? Then you can try to solve my own exercices in astronomy, or in physics ... (please check my videos)

[@Abhaykk1994]

This was fairly simple... I remember the calculus jee problems being much harder. But it's just a question so can't draw much inference on the overall toughness

[@Oldskool_gamer86]

I never did this kind of math before. So it's my first time learning it for college

[@kanguru_]

For the first, just substitute: x = 6 - u and you get an integral which when added to the original integral (I) obviously gives you 2I =2, so I = 1. No formulae to remember. Same for the second problem, where the substitution is: u = pi/2 -x, and 2I = pi/2, so I = pi/4. For the last problem, substitute: u^3 = log12 - x^3, and use the same technique to show 2I = 1/3 * log4/3. This is much simpler and straight from first principles.

[@sayannitdgp8957]

This is some light years away from iit jee level and even jee main level.... These are now not even asked in board exams in India😅.......

[@deepthakur14916]

Please make more videos on problems previously asked in JEE examination!!

[@priyanksisodia5889]

I am now in iit and watching this remind me my tough time.......

[@b12abhaypatel7]

I am an aspirant of aiims. Though our routes can be different but it needs same effort.. Can you just tell me how to increase my siting time

[@shahswatpandey5427]

Hi bhaiya.. Giving jee tomorrow.

[@priyanksisodia5889]

@@shahswatpandey5427 tomorrow?

[@shahswatpandey5427]

@@priyanksisodia5889 yes bhaiya. Jee Mains Feb attempt. There will be 4 attempts each months.

[@priyanksisodia5889]

@@shahswatpandey5427 oh! So just relax, and do not study today . Don't put yourself under pressure. And all the best junior! And do tell here how you did😁

[@monrealis]

Never heard of this formula before. If you don't know it, you're doomed.

[@Konsistori]

Indeed. These questions seem to ask "do you know this formula" instead of "are you smart enough to study here".

[@danielgates7559]

Antti I would argue that these questions are more of seeing the symmetry behind. Making observations is a key part of mathematics. Noticing different parts of symmetry is valid a test for “smartness”, because if you are remembering the formula for each type of symmetry question, there are so many variations and you probably need to remember a lot of formulas. Rather, seeing the innate symmetry hidden behind all these seeming different questions leads you to discover the question-specific formulas by yourself. I personally solved all integrals presented in the video without knowing the formula before. The first one sqrt(x)/sqrt((6-x) - sqrt(x)) is written in such a way that is almost asking for u substitution u = 6 - x. These questions are blatantly OBVIOUS for anyone with some elementary training with symmetry. And these questions, as a test for the participant’s sense of symmetry, are well-made.

[@clashwithanonymous3979]

@@Konsistori smart student can make formula instantly

[@anuragmishra3227]

@@Konsistori It has been made into a formula due to the objective type questions in the exam. It's just an extension of the property that integral a to b f(x) dx can be written as integral a to b f(a+b-x). We are just taught this property and the rest is up to the student in what form they want to remember it.

[@juyifan7933]

You are not doomed, the "symmetrical" nature of the integrals is obvious, using a simple substitution is the first thing that comes to mind if you ever seen this idea before. I never seen this formula, and probably the overwhelming majority of students taking the exam didnt either, but the fact all integrals had basically the same structure is an obvious clue. If they wanted to make the problem significantly harder they would remove the first 2 integrals and leave just the third, that way they wouldnt clue you in that there is a general idea.

[@dmitrystarostin2814]

One of the key formulae we were taught is math class in 7th grade (sic!). The problem is it rarely comes up in reality, but as a mathematical abstraction, it is excellent.

[@AdityaBhoite1403]

No... This is actually a board level question, u will find this question in 12 class board book . Also JEE MAIN is the first exam and then comes the real terror, JEE ADVANCED. Jee Advanved is precursor to admissions in IITs

[@abhinavprajapati5962]

LMAAOOOOOO i was sitting in my coaching (day long) and was kinda tired and my teacher came to me and say do these questions to "relax"

[@dineshloitongbam7734]

Dude found out the way to get views.😂😂 Still one of my fav channels.

[@benryan7586]

Shouldn’t feel good about completing the questions in 35 minutes. But I do. 😂

[@sitharthasg7402]

Easiest question in This channel 👍

[@JDsane]

Can someone explain me 3:01 step of √(cos) = f(π/2 -x) What is f it is sin or can you rewrite this with some explanation please....🙏

[@vat1n456]

We know that sin(pi/2 - x) = cos(x) by the trigonometry. Here, f(x) = sqrt(sin(x)). So, sqrt(cos(x)) = sqrt(sin(pi/2-x)) = f(pi/2-x)

[@ryzzkyle2386]

Piece of cake. Solve some Jee Advanced questions.

[@godson200]

This is ncert damn it... Guys children solve this in class 6 and class 7 .. I.e. age 10

[@ishan4691]

@@godson200 were you high or something while writing this?

[@ramanunnikrishnan7354]

@@ishan4691 Some people do, I had a friend who had mastered Permutation and Combination at 7th grade,

[@GoD_LoRD04]

@@godson200 not at all

[@nityasingh3]

If you can't solve this in seconds... You haven't studied definite integral

[@aishwaryar1290]

Yupp

[@nikhilnagaria2672]

Big no

[@avneesh690]

Le jee mains: Ahh I am bored from this😂 Le jee advanced: Hold my beer😂😂

[@Thomas..Anderson]

So this exam depends on either you know an obscure formula by heart or don't. This kind of exam do not promote creativity but mechanical repetition. One of the reasons why Boeings 737 fall out of the sky.

[@majapahitsumatra5771]

Two years into NIT, I've still solved them just looking at them, Keys are replacing variable with sum of limits - variable, adding initial expression with final expression, num = den, result = 0.5(diff between limits)

[@aninerd1321]

These questions come in the category of very easy questions in jee

[@lollel1490]

Indians I would like to to inform you that no one actually cares how hard the Jee is

[@bhujiamonster3471]

I would recommend you to solve Jee advanced indefinite integrals questions.

[@Nobody-pv9jt]

It would be an hour long video for this guy lmao.

[@saadrizvi6630]

You have to first master the chapter functions, 90 percent of engineers can't even find the range of a given function I can bet that

[@bhujiamonster3471]

@@saadrizvi6630 They need not either. When you got desmos, wolframalpha what's the need to be able to find it.

[@Nobody-pv9jt]

@@bhujiamonster3471 ikr it's like saying 90% of the mathematicians can't calculate the log of 48397 without a calculator lol.

[@bhujiamonster3471]

@@Nobody-pv9jt No mathematican should be able to calculate it. Even with calculator. Its irrational 😅😁 Edit: fixed spelling

[@prerakcontractor6609]

To the people who are complaining about this formula, it actually has a much deeper meaning. It consists of the same method we use to evaluate sums like (1+2+3...+n), i.e. by adding the sum and its reverse: S=1+2+...+n S=n+...+2+1 2S=n+1+....+n+1+n+1=n(n+1) S=n(n+1)/2 similarly for the type of integration given in the question, we can see that it is like a sum of very small elements. And if we add the first and last term, second and second last term and so on.... we will always get 1, i.e, f(a)/(f(a)+f(b)) + f(b)/(f(a)+f(b))=1 and so on. so we get, 2I=1(b-a) I=(b-a)/2

[@amayjha]

5:28 since U is equal to some constant minus X. So can we write U= X. Please reply me.

[@jasonscott1594]

These integrals are a little trickier than what we've seen so far, do you guys see why? It's a little subtle but it's there. This integral is... Located on the BACK side of the lookup table, exactly. Difficulty level 632 am I right?

[@Noname-cp6rn]

Huh... that's soo easy...pleaee take harder problems from JEE Advanced set of IIT JEE ... Thank you😅✌️

[@dnhdfnfkrjxjxfjjggj3002]

It is a board levels problem

[@anandk9220]

@@dnhdfnfkrjxjxfjjggj3002 Can anyone solve the following questions please? I'm trying a lot but don't have clear idea as of now. Question 1 - Integral from 1/2 to 2 of { x + 1 - (1/x) } × { e^ [ x + (1/x) ] } dx Question 2 - Integral from 0 to pi/4 of { sin [ x - (pi/4) ] } dx ÷ [sin 2x + 2(sin x + cos x) +2] I came across the above problems on toanmath.com. Thank you.

[@SuchetanSaravanan]

These are much simpler which used to be asked in AIEEE. The current JEE mains is much much harder.

[@ashutoshmishra7429]

Oh yes . This rule is also known to as "KING'S RULE "

[@BCS-IshtiyakAhmadKhan]

@@ashutoshmishra7429 bhai kota me padhe ho kya?

[@ashutoshmishra7429]

@@BCS-IshtiyakAhmadKhan nahi bhai

[@armaangogoi7468]

Same type of question came in 24th Jan 2023 shift 1, so easy questions also do come :)

[@yashvardhanrao3182]

The trick when to apply this king rule is that you should look for denominator which wouldn't change its value after applying the rule Like in the question given in video

[@Modemon57]

take the middle point of a and b as C .. and let x' = a+b-x; So for each x , x{a

[@zakariaismail2258]

"Solve in seconds" They didn’t tell exactly how many seconds just to be on the safe side

[@venkatbabu186]

Wave means varying ratio. Root plus root means reduction of frequency. Integral means expanding frequency.

[@rasigadhanya8952]

This is the easiest question in IITJEE .come on, i've seen many questions more complected than that

[@newmood24]

1) This is a basic Integration problem given in NCERT Maths class12, which is the easiest book of 12th grade maths in India 2) By qualifying jee mains u dont get into IIT, if you score good then you will be selected for jee advanced exam after which you get iit if you get enough marks..nearly 1million students appear in jee mains exam,150k in jee advanced and 10k students get IIT. 3)Jee advanced is not a piece of cake, applying and memorizing these simple formulas will never help you in passing Jee advanced, however you may be able to get through jee mains with low marks.

[@sumzk]

You need to realise the curriculum is different in different countries , SAT was probably the easiest test I've done till date and I've seen people asking strategies for that. Being Indians we are exposed to this and we learn stuff at an earlier age, it's nothing great

[@newmood24]

@@sumzk For some it is great, for some it isn't. Considering the reasons of my statement to be very simple, I dont want to go deeper in this.

[@xanderstefan3396]

For those of you saying - "you either know this formula, else youre fucked" this is a misconception! The truth is, this formula is literally everywhere in our textbooks, and many examples are there based on this very 'formula' . It absolutely doesnt mean that India is better than others , or others are better than India , truth be told , all of us are equal when we are born , what we do later distinguishes us Picture this: You have a book which explicitly states the use of this 'formula' several times , and youre pretty used to seeing such questions in simple examinations, and all of a sudden the same formula which is literally everwhere in our books pops up in JEE as well , its gonna be darn easy cuz, well its literally everhwere Totally understand that this isnt taught in America/Europe/Africa - hence it seems like this formula has come out of the blue Assume your lecturer in Europe/America/Asia/Africa gave you a very interesting problem in class , and you enjoyed it thoroughly , and somehow the exact same question popped up in your exams as well! It would seem very easy to you because youve already done it. Give the exact same problem to an Indian and he may struggle , possibly even give up, or take a lot of time and give the answer. Thats exactly whats happening here, this question which came in JEE was a matter of sheer luck that many students have already seen something like it !

[@jayw4366]

the saying is true ..."you need an indian to help solve an indian question"

[@asheeeshh]

This isn't even boards level I literally can solve it in 10 seconds just using property of definite integral.

[@rustcohle57]

Exactly

[@rahulrajss723]

Exactly, Even me too...

[@dnhdfnfkrjxjxfjjggj3002]

Me too

[@seanleith5312]

India? next time, get something from Ethiopia.

[@lakshyamalik7896]

I did that. all were solved with same property

[@abhilashgeorge3317]

Bro these questions we get for test paper😂😂

[@gouthamm2005]

1:40😯Vedantu is world famous

[@christianacacia5127]

With sin above or cos above give the same result ==> its direct without your formula. But its an elegant formula wich has a very greater domain of aplication. Thanks

[@nishantdesai3705]

please guys calm down stop bragging about how hard IIT entrance exams are, no one is going to give you an award for it.

[@prathamr7935]

Yes sir u r true But did u quality iit advanced If not I suggest you take ur post down

[@nishantdesai3705]

@Chinmay Hegde everyone knows that obviously entrance exam of a country's best University is going to be hard, do you see people bragging about how hard Stanford or MIT exams are ?

[@Nobody-pv9jt]

"I don't like what you're doing so stop doing it and even though I could have just scrolled past/ignored your comments I'm just gonna make a comment about how butthurt I am instead" K.

[@nishantdesai3705]

​@@Nobody-pv9jt everyone else "huh, I ampreparing for IIT exams or I have cracked IIT exams how can I show off how smart I am because literally no one else is acknowledging me, oh I know let me shout at the person who made a video who has at least did some work, let me shout at him about how easy these questions are (which anyone who's serious can solve by preparing for a week) which will show how smart I am"

[@Nobody-pv9jt]

@@nishantdesai3705 more like "lol this guy actually made a big deal out of literal ncert questions let me just clarify that JEE isn't that easy in the comments"

[@ayush-sp6xr]

All my ans. are correct My exam is on 9th jan. Jee mains Preparing ....... Plz bless me

[@zackz7497]

Only one question will come from definite integrals

[@CCCharles45]

hope your exam went well :)

[@thelegendsofbaihatacharial8222]

Gives board questions Says jee main questions Talks about getting seat in iits. Really????

[@uplink-on-yt]

I'm watching this channel for entertainment purposes. I don't understand much of what you say, but it's awesome.

[@kravisha1]

how did the limits of integration flip at 5:17 ? we are still having the -du right?

[@notdave.39yearsago67]

When we change the variable we have to change the limits accordingly. x --> (a+b)-x Therefore, b --> (a+b)-b =a a -->(a+b)-a =b

[@kravisha1]

@@notdave.39yearsago67 Ohh yess !! How could I forget that.. thanks for taking the time to reply to me.. cheers! My respects and love go to all my teachers, who have kept the passion alive in me..

[@anirie6747]

JEE 2020 aspirants all the best!! ❤

[@maxmunch925]

You ain't gonna make it to IIT dear

[@simarpreetsingh7235]

@@maxmunch925 tu hogya?

[@maxmunch925]

@@simarpreetsingh7235 ha

[@vijay5905]

These are in my maths ncert book I had done these in second 😜

[@kritik8837]

As expected comment section filled with Indian comments giving him information about jee advanced

[@maartenwestermann8229]

What I would like to learn from math problems like these by a site that calls itself “Mind your decisions” is: Besides solving these problems, what decisions will it allow me to “mind”, or make or take? What practical, world or daily issues will I be able to solve better, quicker or easier once I know the math rules behind these problems? Because that would be truly handy.

[@constipatedbowels3473]

There is no need to memorise this formula as many people claim....This can still be solved in a few seconds even if we don't use this obscure result..... btw this obscure result is a consequence of applying King's property of Definite integration,which can be derived from very mundane substitution..... in JEE main,students get only 2 minutes to solve such a question ,hence they need the formula.....This test tests for accuracy and speed and not mathematical acumen which is tested to some extent in the next exam ,JEE Advanced!!!!!.....