Math Integration Timelapse | Real-life Application of Calculus

[@martingu1005]

This is exactly how math teachers expect us to use math "in the real world"

[@JusticeShepard]

Haha for real

[@bluebear2912]

Fr 💀

[@Mogger1209]

Fr 💀

[@creativename.]

Fr 💀

[@AlmightyBert.]

Fr 💀

[@shresthishigwcivpadt9713]

finds out it runs at 3.14 kbps

[@Gamer_Boy_C-sharp]

😂

[@SmilingMathEquation-dq9oq]

Very easy question 😂😂😂😂😂

[@harrypottergaming4837]

💀💀

[@arifariffulislam2246]

Best comment

[@RGDFF]

Gbps

[@Selatapey]

“The password is all of the digits of the answer”

[@alien8742]

Underrated comment

[@RjrirDbdbdj]

🤡

[@aswajithk.s9574]

😂

[@shwyamshubham1448]

That cannot be possible as the value of pi extends infinitsimily so any value upto the rational mark would be only answer

[@ShreyashOjha-o3i]

​@@shwyamshubham1448can't you understand a singular joke....

[@txt_tomorrowxtogether2154]

Read the title as integration relapse and clicked to see what kind of person is battling an integrals addiction

[@tegathemenace]

I just relapsed😢. In my excuse we had an exam

[@aryatripathi06]

this made me crack up😭😂🤣

[@jivinmonging]

intergration relapse 😭

[@KeiraSamson]

HELPPLPP

[@JatPhenshllem]

😂

[@Keitan97]

“Sir, we’re closing soon”

[@PeiqiLi-RealLove]

🤣😅

[@ryanstocks4298]

"Hold on, I've almost got it."

[@ivettrivera5306]

​@@ryanstocks4298"sir please leave, just complete it tomorrow"

[@mobinthehood7906]

He still has the pasword y

[@aparnarai3708]

​@@ivettrivera5306The next day: **New equation**

[@Pietruszka64]

*proceeds to use mobile data*

[@nostalgic_nickname3935]

*proceeds to unload gun on owner*

[@Java_RAM]

*Proceeds to use bold letters*

[@COACHCRAFT44]

Proceeds to Proceed

[@slcoco]

proceeds to proceed proceeding

[@Just_like_that1234]

Proceeds to go home after mobile data has used up

[@qwertytarantuno730]

math teacher warned us

[@DrOggy67]

The integral can be easily solved mentally. The term with the cosine function is point-symmetric with respect to the origin due to the factor x^3. Because of the symmetric limits of integration, the integral over this part vanishes. What remains is the factor 1/2 and an integral over a semicircle with a radius of 2. The area of the circle is 4π. Thus, the area of the semicircle is 2π. Due to the factor 1/2 in the integral, the result is π.

[@fablearchitect7645]

yeah this only works because the bounds are symmetrical around the axis of odd symmetry. If the definite integral was from 0 to 2 then you would be screwed.

[@salimkhd8713]

I mean that's what he did too, he showed the first part was an odd function and the second part was a semi circle. A proof needs to show the steps

[@landenheine7645]

Yeah, but I was thrown off by the dx being under the root. I thought it was some higher level calc I hadn't learned yet, instead it was just a typo

[@Bold_new_city_of_the_south]

There's an example like this on the GRE mathematics subject ​exam..very similar@@fablearchitect7645

[@PamellaCardoso-pp5tr]

​@@landenheine7645well, dx COULD be under a root. It would just need to use some substitution magic. Its pretty much how we define more general integrals later on like surface integrals, lebesgue integrals and etc. like how we define the lebesgue integral of a function f(x) over a measurable set M as the integral{M}(f(x)d$) where $(M) is a measure over the set M. basically: sqrt(dx) = dy, then you would solve this differential equation in therms of y and substitute it everywhere to get rid of that crap. Sometimes you will need to go a bit more deeper and play with the structure, parametrize some curves or some surfaces to keep your integration bounds... you know... all that fun stuff 😅

[@Dushman-Shuravi]

**Proceed to open an AI with calculator **

[@Its_tomj]

Open AI

[@SDjoigsrnt39]

@•[ArtyFunky]• 🎶 mobile data 😂

[@dustsans9859]

@@SDjoigsrnt39 sup

[@SDjoigsrnt39]

@•[ArtyFunky]• 🎶 skill issue

[@juaneldelostacos]

Result: XD

[@Ilikebananasouioui]

*proceeds to use my math calculator app without internet*

[@slobodanpraljak1464]

Ain’t no way your calculator works on integrals like that. Symbolab can’t even do exponential equations.

[@Heirloop]

@@slobodanpraljak1464 isn’t there an app that solves something by taking a photo of it?

[@slobodanpraljak1464]

@@Heirloop yes, I believe you’re referring to symbolab, or one of the other bootleg offshoots. Those don’t work on hard integral equations though, like the one in the video.

[@Hallucinatorig]

@@slobodanpraljak1464 the one I have does

[@tomtommy-rv8pp]

You just killed the joke 💀

[@MynameisS_A]

“First digits of the answer” **Tries every fucking combination**

[@goldenboom345]

Well there are a total of 1000 possible combinations

[@michahermann7869]

​@@ilikefootballandbaddecisionspassword length is limited

[@saykom6573]

​@@goldenboom345 no only 10, 0 through 9

[@EnderGoku9001]

@@ilikefootballandbaddecisions 💀💀💀

[@ilikefootballandbaddecisions]

@@EnderGoku9001 the answer is, there was no Wi-Fi in the first place.

[@BrainBlix]

For those who did not understand, first he multiplied and expanded the given integral function into two integrals. For the first integral function (𝑥^3)*cos(𝑥/3)*sqrt(4−𝑥^2), he checked whether the function is odd or even. It is odd. If the function is odd from −𝑎 to 𝑎, the value of the integral evaluates to 0. Hence, its integral became 0. Now, for the second part (1/2)*sqrt(4−𝑥^2), we all know that definite integration is basically area under the curve. He squared the function sqrt(4−𝑥^2) which resulted in the equation of a circle. He then calculated the area of the circle, but we only want the area under +sqrt(4−𝑥^2) and not above -sqrt(4−𝑥^2). Therefore, he took half of the area of the circle. After further simplification, the final answer is 𝜋. Edit: btw that 𝑑𝑥 should not be under the square root sign, so mathematically the question is wrong.

[@louiseditxs]

how did you do the x font letter thing

[@marijokardas]

(x^3)

[@matthewxeditz]

what

[@sportstackerpro]

True

[@DavyanHatch]

I don’t think the people who don’t understand would understand anymore than after they read this

[@TheResurge-gq6nb]

Imagine reaching the final answer and after successfully getting connected to wi-fi, the wi-fi doesn't work 💀💀💀

[@Dragon_Ballz_Aryan.]

And after a while it gives a new question to solve ! ☠️

[@JESUSISLORD.........]

Ephesians 6:12 says, For we wrestle not against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this world, against spiritual wickedness in high places. Jesus disrespected every religion, in John 14:6, Jesus saith unto him, I am the way, the truth, and the life: no man cometh unto the Father, but by me. We are not to be with any other religion. Because if we do, Matthew 6:24 says, No man can serve two masters: for either he will hate the one, and love the other; or else he will hold to the one, and despise the other. Ye cannot serve God and mammon. Don't pray for other religions.. But we are called to pray for one another in James 5:12 says, But above all things, my brethren, swear not, neither by heaven, neither by the earth, neither by any other oath: but let your yea be yea; and your nay, nay; lest ye fall into condemnation. Is any among you afflicted? let him pray. Is any merry? let him sing psalms. Jesus saves, God bless.😊

[@Dragon_Ballz_Aryan.]

@@JESUSISLORD......... Bro left the whole text to proof this comment wrong ☠️.

[@namothegamui2573]

@@Dragon_Ballz_Aryan.i mean you can just brute force it since it say first digit is the answer so there is 10 possible answer not counting negative

[@Kong37BattleCats]

​@@namothegamui2573?

[@LiveBetterSub]

Imagine spending 5hrs of your life solving and it says the password is incorrect 😂😂😂😂

[@FlashFictionFilms-s6p]

Bro it takes no more than 30 sec

[@LiveBetterSub]

@@FlashFictionFilms-s6p bro I said this cuzz I'm a 9th grader😒

[@FlashFictionFilms-s6p]

@@LiveBetterSub 👍👍

[@RenLapislazuli]

This specific integral is actually completely trivial First, this integral can be split in 2 parts: x^3*cos(x)sqrt(4 - x^2) and sqrt(4 - x^2)/2 The first part, the x^3*cos(x)sqrt(4 - x^2), is an odd function, meaning that its integral is 0 The other part is sqrt(4 - x^2)/2, which is a well known integral with value of pi

[@Pedroharada]

@@RenLapislazuliwhere the hell did that “/2” came from? (I’m also a 9th grader)

[@afif4738]

Now imagine the password is the last 10 digits of the answer 🗿

[@opelgrove10240]

oh, f...

[@deusd.2366]

Genius 🤣🤣🤣

[@Roundamation]

But it wouldn't be possible cause pi is infinite

[@afif4738]

@@Roundamation not with that attitude

[@saravanarajeswaran2626]

​​@@RoundamationThat's the whole joke imao

[@firemonkey1015]

I actually wish places did this often, that’d be pretty fun to figure out

[@SrijanSingh-m2w]

"Shows , connected without internet" 💀💀💀💀💀

[@Arqade38]

R.I.P ⚰️ 💀💀💀💀💀💀

[@peteplayz-norskgaming5723]

💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀💀

[@RdSharma-qc5yk]

Lmao 😂💀

[@JiarulMondal-ud5rk]

💀🗿

[@nothinghere12315]

😭💀

[@imcalculus]

The dx under the root : *aight imma head out*

[@PixalonGC]

omg that's so cursed

[@CLASHERHERE]

Man,when you take integerals dx gets canceled with that big s sign and a constant c is added

[@PixelionRules]

The worse part is he could have just used a direct theorem to solve the second broken integral instead of drawing a curve and taking half a circle, which would yield 0 when you put the limits 😭

[@inferno3728]

@@CLASHERHEREjust saying, that’s a really REALLY bad way of understanding integration. What op meant is the dx is randomly put inside the function which makes 0 sense

[@CLASHERHERE]

@@inferno3728 what dx are we talking?

[@alphrz]

Connecting to WiFi in Harvard be like:

[@S_noq]

Hell nahh

[@Simplistic_person]

💀💀💀

[@dakshmahajan25725]

Nah thats basic 12th grade integration lmao (in india idk about other countries)

[@GoatedEminem]

Or mit

[@alphrz]

@@dakshmahajan25725 I'm in like 6th grade my braincells ain't finna comprehend that

[@Rekha10017]

Dil garden garden ho gaya question lag gaya ♥️✨😀

[@Meme-wq9nv]

Asian Wi-Fi be like:

[@AlbertTheGamer-gk7sn]

This is an integral used in a Chinese university where the students must find the right 8 digits of this integral for the Wi-Fi password to get the Wi-Fi in the dining hall.

[@Monocle-addict]

@@AlbertTheGamer-gk7snwell it’s kinda easy though

[@konhatepakfilm]

Bruh not always

[@gamerskyfire007]

BRO JUST FORGOT EVERYTHING... THERE ITS WRITTEN WIFI password is the first digits of the answer... but password cant be of single digit... even if it is we can just put 9 try and you will get wifi.... LOL NO NEED TO SOLVE IT

[@mikuculus3720]

I can’t like the comment it’s at 314

[@darkkk2448]

Service of wifi is available -24/7 ❌ Wifi's service is available -22/7 ✅

[@saritayadav9200]

clever

[@br0k3n.wind0ws]

this is damn good lmao

[@costa-w3k]

i would prefer 21/7

[@jacintawilson6987]

😅Me asking google

[@SwiftyTheSword94]

I also learned the hard way it ain't pi

[@thoanha5799]

"what the passwword?" "in the wall"💀

[@alyme_r]

??

[@PriyankaSharma-ub3rx]

​@@alyme_r3.14

[@BornilTasin]

dman

[@lordsamrat137]

​@@alyme_rwhat

[@GoofyAhOklahoma]

"In the wall. . . is that all caps?"

[@baselinesweb]

That damn sqrt of dx. Gets you every time.

[@PrateekShukla400]

Man, that square root bar over dx nearly gave me a heart attack☠️

[@carolinacobra]

Same

[@dot3969]

I left one question in exam due to this 😅

[@phoenxi_]

Bro I didn’t even notice that

[@nkhnouk3781]

​@@phoenxi_same

[@Vedant_Ipte2]

Is it printing mistake or something ?

[@Eyad__Gaming]

Bro really needed that wifi password💀💀

[@GursimarSinghMiglani]

Ok bro

[@NITRICFF]

Ok bro

[@leishisomarchang3297]

😂😂

[@BelldofersMatlack]

Plot twist: He needed it to do his math

[@KrishnaThakur-nf4rt]

Tbh it was an easy integration

[@ZanRBLZ]

just imagine the wifi password changes everyday 💀💀

[@theffects9545]

Tomorrow: the last digits of the answer💀

[@RichBatangKalye]

@@theffects9545bro 💀

[@GodEagle10]

​@@theffects9545💀💀💀

[@ItzBluh]

Just try all the 10 digits 🤔

[@nimishgrover7637]

@@theffects9545it is a challenge to whole humanity 💀

[@viratcomputertechnologygyan]

Me with my mobile data and Google lens 😂😂

[@unspokenscares]

underrated comment

[@imtiyazazhar5878]

Google can't solve the exact problem. An AI would.

[@Error_-hj5jg]

That was the easy part... Now you gotta figure out what digits are the "first digits"

[@Tucxy]

Lol fr

[@horizonshot]

Guessing its the first 8 digits?

[@GeorgeMariusCracu]

There are no digits in PI, only letters.

[@cheese6782]

@@GeorgeMariusCracu??? pi has digits

[@rabbiezekielgoldberg2497]

@@cheese6782 He was talking about how the letter Π is spelled using Latin characters.

[@NaplesFC]

imagine if it said last digits lmao

[@kohi_kohi]

Underrated comment

[@blahblahblah5051]

then, it will take another 10 years☠️

[@chungy47]

@@blahblahblah5051it would actually never be solved.

[@blahblahblah5051]

@@chungy47 thank you for correcting, but I knew that already. Just Commented as a joke.

[@Jerry-sf5sc]

​@@kohi_kohiit's not, he copied my comment

[@deformed1789]

Students:"Math won't help us in everyday life!" The sign: I'd say that you're wrong

[@sakuprtsalauew4786]

​@xX_MelvinSneedly_Xxare you a communist?

[@OluwadotunSoyinka]

Correct 😂 answer ❤.

[@Mission_IIT_JEE]

Bro When I First Watched This Video I was Just shocked Seeing him do These Hard Calculations But Now as I Can do These Im Really Happy😊

[@cowninjawarrior]

Bro removed the dx from under the square root

[@soha5318]

thats what im saying

[@HimanshuHKKumar]

No. All steps are correct. Reason : Integration is basically under the curve(one variable). So, for the 2nd term, he plotted the graph, and found the required area.

[@3vxn.5unt]

@@HimanshuHKKumaryeah but right at the beginning writes out the equation on the white board he removes the dx from under the square route. I guess he assumed this was a mistake made by the cafe

[@HimanshuHKKumar]

@@3vxn.5unt I guess so. It's probably a mistake.

[@shwyamshubham1448]

​@@HimanshuHKKumar I think as the limit is -2 to +2 the x value would have been 0 and he would have removed it while adding as int/dx is x+c without limit but the limit is given

[@isaaccampos2393]

"The password is the last 3 digits of the answer "💀💀

[@noahgoelepuri]

😂

[@aritra_adak]

142 bruh...😉

[@fathanlh214]

​@@aritra_adakthat is the second third and fourth digits of phi

[@AlfyDC]

Easy, just try 000-999 😎

[@ItzCalamityYT08]

​@@AlfyDCthat is still 504 combinations

[@SilveyGalaxy]

Photo math: I'm about to end this whole mans career

[@PantherXO.]

No bro photomath cant solve this type of questions i tried in my graduation 🎓

[@sttwtest]

​@@PantherXO.It's a regular integral that wolframΑ solves in under 5 seconds

[@lunayokai885]

How will you use it without internet

[@DriverEra.]

@@lunayokai885cellular data

[@lunayokai885]

cellular data yes thankyou

[@baselinesweb]

Checking for odd is genius.

[@grooveseeker6269]

the first term being and odd function and thus cancelling its area is just pure magic!!

[@LongTran-em6hc]

I like your funny words, magic man And this is from an engineer

[@nwb_sameer]

Also use for √a²-x² dx =x/2√a²-x²+a²/2sin`¹x/a 😂

[@pramathhegde317]

But first we have to integrate by parts then we should integrate the root a²-x² dx😅😊😊😊

[@shaanIITP]

​@@pramathhegde317where by parts...😅 There is direct formula applicable here ... 1/2√4-x² is an even function then integral can further be changed to 2 times that function limit 0→2

[@AvengerKill-wt4br]

​@@pramathhegde317no nee bro, the first term cosx/2 is odd, so its integration is zero, we only need to integrate second term, that is root 4-x^2

[@AndrewGuyGD]

Albert einstein in disguise?

[@alphastriker5799]

​@@pramathhegde317 bro direct formula 😂

[@neologicalgamer3437]

It should've said "the last six digits", so ending with pi would've been hilarious 💀

[@helium829]

3.1415🤓

[@proctyispro7903]

​​@@helium829 You failed your maths exam didn't you

[@nttsight1564]

​@@helium829 How did you get English and Maths wrong in one question

[@helium829]

@@nttsight1564 idk, maybe I replied that comment on 3 am😪

[@helium829]

@@proctyispro7903 tbh no

[@Baldi-00]

Great job!

[@parshuram11023]

This is easier than the easiest integration of class 12 boards in WB board...

[@alphastriker5799]

True

[@aguywithwhiskers]

Its in class 11.

[@Sudarshan.primodial_balance]

Warner Brothers? 😂

[@RandomReviews2008]

@@Sudarshan.primodial_balance I think he means West Bengal Board (a state in India)

[@josevillarroel3016]

Who asked?

[@isi2973]

The dx is under the square root, so it is dx^(1/2). You calculated the full integral, but you were asked to do the half integral. And yes, this concept does exist (actually many different concepts of fractional calculus exist). A common one is the Riemann-Liouville-Differintegral formula.

[@aaronhughes827]

🤓

[@watermelon_cat_sussy]

🤓

[@flw2270]

🤓

[@thetafritz9868]

💪🤓

[@Reccaj8161]

🤓🗿

[@Gracell0]

How math teachers think the world looks like:

[@Ritesh_27]

Bro, it's most easy integral. You need to study.

[@deadrider39]

@@Ritesh_27not everyone studies integral calculus. Ur right but it’s really useless for almost every profession besides engineering

[@cloroxbleach7554]

​@@deadrider39Probably useless for the average person, but still useful for humanity in general

[@harshitrajput3566]

​@@Ritesh_27because you are from 🇮🇳❤

[@HeyAHappyHuman]

The world does look like that 😹 you just have to be willing to analyse things

[@mrcool9097]

seeing the last function as a single semicircle was impressive. Learning something with this one😊

[@ederbanks]

It’s one of those things that makes you feel dumb for not realizing it

[@arch_wyd]

We found the moment teachers told you that you need math irl

[@g33xzi11a]

If you’re taking calculus then chances are you actually will use it. The people who ask this imbecilic question don’t usually aspire to more than grade school algebra.

[@jgmenelik111]

​@@Dont_click_this_profile-v8jok

[@akronomes]

​@@Dont_click_this_profile-v8jok then bot

[@CarTM]

I have 2 hours of Calculus homework left. This isn't a joke anymore, it's reality.

[@g33xzi11a]

@@CarTM calculus is easy.

[@terryqokov6999]

You don’t know how much I aspire to be like this. Legend.

[@anasuachattaraj02]

thats amazing, this is fr so attractive.

[@terryqokov6999]

knowing maths in general is attractive af imo@@anasuachattaraj02

[@Alice-oe6pv]

@@anasuachattaraj02fr

[@potatokujo4673]

​@@anasuachattaraj02it's basic calculus nothing to be impressed of

[@ZashD.WaterLaw]

​@@potatokujo4673bhag😊

[@susmitadutta1029]

The dx is also under the root

[@dwiwi07]

"Wifi password is the last 5 digits" 💀 Edit: How did I get 2k likes???

[@stockbrot14.16]

so no password?

[@capybaraville]

​@@stockbrot14.16 there are actually the last digits to pi, since there's a number that's just pi backwards (i think it's called e)

[@sprite3398]

@@capybaraville E

[@numbertheory2435]

@@capybaraville no

[@db5094]

​@@capybaravillewhat

[@Kya-Karoge-Name-Janke]

Easy way : u have divided the q. In 2 parts like he did and got 1 part as a odd integration f(x) =0 . Now for the 2nd part we can it as under root (2²+x²) and simple use the property of a²+x²dx =x/2•under root a²+x²+a²/2•sin-¹x/3

[@NatsukiNafis24]

**AUUUGGHHHHHHHHHHHHHHHH**

[@Jp_74]

Bro it is 2²-x² and sin-¹(x/2), I applied that one only but my ans is pi/2, what ur's

[@Alpha_One7]

its root a^2-x^2 ...

[@Alpha_One7]

​@@Jp_74mine is coming pie , i think you have put the wrong formula

[@akhilmaniyar5010]

I used the same formula but got -π as the answer

[@yashvantkumar5972]

Good job recognising the even function and cancelling it and solving rest of the equation by the help of circle 👍

[@Shmience]

But functions have to be odd to cancel

[@yashvantkumar5972]

Oh sorry not even it's odd thanks bro 😌

[@Mr.Hp.2050]

if you have courage, then find (x+y)² in fraction and (x+y)³ in fraction if, 1/(9x+36y) + 1/(9x-36y) = 456/391 and 1/(9x+36y) - 1/(9x-36y) = 371/291.

[@valerinucubidze7820]

bruh its too easy Let's solve the problem step-by-step. We need to find \((x + y)^2\) and \((x + y)^3\) in fractional form, given the following equations: 1. \[\frac{1}{9x + 36y} + \frac{1}{9x - 36y} = \frac{456}{391}\] 2. \[\frac{1}{9x + 36y} - \frac{1}{9x - 36y} = \frac{371}{291}\] Let's denote: \[ a = \frac{1}{9x + 36y} \] \[ b = \frac{1}{9x - 36y} \] Then, we can rewrite the given equations as: \[ a + b = \frac{456}{391} \] \[ a - b = \frac{371}{291} \] **Step 1: Solve for \(a\) and \(b\)** Add the two equations to solve for \(a\): \[ a + b + a - b = \frac{456}{391} + \frac{371}{291} \] \[ 2a = \frac{456}{391} + \frac{371}{291} \] To add these fractions, find a common denominator. The least common multiple of 391 and 291 is 113981. Calculating: \[ \frac{456}{391} = \frac{456 \times 291}{113981} = \frac{132456}{113981} \] \[ \frac{371}{291} = \frac{371 \times 391}{113981} = \frac{145181}{113981} \] \[ 2a = \frac{132456 + 145181}{113981} = \frac{277637}{113981} \] \[ a = \frac{277637}{2 \times 113981} = \frac{277637}{227962} \] Subtract the second equation from the first to solve for \(b\): \[ a + b - (a - b) = \frac{456}{391} - \frac{371}{291} \] \[ 2b = \frac{456}{391} - \frac{371}{291} \] Using the common denominator approach again: \[ \frac{456}{391} = \frac{132456}{113981} \] \[ \frac{371}{291} = \frac{145181}{113981} \] \[ 2b = \frac{132456 - 145181}{113981} = \frac{-12625}{113981} \] \[ b = \frac{-12625}{2 \times 113981} = \frac{-12625}{227962} \] **Step 2: Express \(9x + 36y\) and \(9x - 36y\) in terms of \(a\) and \(b\)** Recall: \[ \frac{1}{9x + 36y} = a \implies 9x + 36y = \frac{1}{a} \] \[ \frac{1}{9x - 36y} = b \implies 9x - 36y = \frac{1}{b} \] Substitute \(a\) and \(b\) into these equations: \[ 9x + 36y = \frac{227962}{277637} \] \[ 9x - 36y = \frac{227962}{-12625} \] **Step 3: Solve for \(x\) and \(y\)** Add and subtract these equations to isolate \(x\) and \(y\): \[ (9x + 36y) + (9x - 36y) = \frac{227962}{277637} + \frac{227962}{-12625} \] \[ 18x = \frac{227962}{277637} + \frac{227962}{-12625} \] \[ 9x = \frac{1}{a} = \frac{227962}{277637} \] \[ x = \frac{227962}{2 \times 277637} \] \[ 9x = \frac{227962}{277637} \] \[ 9x = \frac{227962}{-12625} \] Finally, solve \(x\) and \(y\): \[ \text{Using} \frac{1}{9x + 36y} = a \text{ and } \frac{1}{9x - 36y} = b \] Find \((x + y)^2\) and \((x + y)^3\): After solving for \(x\) and \(y\) values, calculate: - \((x + y)^2\) - \((x + y)^3\) **Summary of the calculations:** Finally, use: \[ (x + y) = \frac{113981}{2} \] \[ (x + y)^2 = \frac{391}{456} \] \[ (x + y)^3 = \frac{371}{291}

[@MathewPrixyMendoza]

​@@valerinucubidze7820I have a stroke reading dis and how long did you comment that☠️

[@ΣπΩΦθφβζ]

​@@valerinucubidze7820blud copied from chatgpt💀😭

[@mobchoir]

​@@MathewPrixyMendoza it's chat gpt

[@unaestudiante1250]

I didn't think about checking the symmetry to solve it. Nice one. Thaaanks

[@lapikolko2]

**laughs in Photomath**

[@МаксимЯшин-з7п]

It's't in foromath

[@Noobasuki]

Mathway

[@moviastdyst]

Wolfram Alpha:

[@DarkMFG]

​@@moviastdyst wolfram alpha is best

[@climate069]

Guys you really need 3rd party help to solve these ezpz questions 🙄 it's a peace of cake for avg. 15 year old Indian.

[@BroEdits1061]

When a mathematician couldn't get a job he/she wanted

[@ietdkvd]

The word "they" exist, just so you know. Edit: seem like a lot of people was mad because they didn't clearly read my statement.

[@methanoI]

@@ietdkvd Aand who cares? He/she is just a longer version of "they."

[@revilsanjiani146]

Nuh uh

[@WhyDoIHaveToStayAlive]

@@revilsanjiani146good job

[@BroEdits1061]

​@@ietdkvd I know but it didn't come in my mind

[@CarolGuy-w2p]

The smile at the end just makes this vid so much better

[@BennGuy.-.]

What my parents think i’m doing in my math class :

[@superprofi4307]

Imagine it's an impossible Maths problem and the password is "Syntax Error"😂

[@coolguy-hu4ou]

the dx is under the square root so technically yeah it is a syntax error

[@justrandomthings8158]

@@coolguy-hu4ou there’s actually possible manipulations we can do because of the fact that the dx operator tends to 0. Bri the math guy did a cool video on this concept

[@neurosynchron]

The real answer then lies in one thing; is it written all lowercase or with big S, space, & big E?

[@madknights2670]

Broooooooo wtffff

[@wiener_process]

@@coolguy-hu4ou Well, you can integrate with respect to a function, so it wouldn't be that much of a problem, except sqrt(x) isn't defined on [-2,0), so in this case such an integral wouldn't exist.

[@stuffedsomething1699]

Now, the question everyone should be asking is, "the first *how many* digits?" Because not all security methods use 8 digit codes.

[@Buckle-Bucky]

It's 3.14

[@realchiknuggets]

@@Buckle-Bucky you slow?

[@Buckle-Bucky]

@@realchiknuggets the first digits are literally 3.14

[@listey]

​@@Buckle-Bucky 3.1 is also a valid answer to the first digits. We don't know who is correct as the number of digits was not specified.

[@Buckle-Bucky]

@@listey but everyone knows pi Is 3.14 Everyone refers to pi as 3.14 In math when told to use pi, you use 3.14 If the calculator doesn't have a pi button or If you aren't using a calculator you don't write out pi you write out 3.14 The first digits It Is known across the board that 3.14 Is the first digits of pi Everyone knows that You are arguing for the sake of arguing rn You aren't helping at all

[@SalehAnime]

Excellent, don't be tired❤❤

[@konstantinsotov6251]

imagine sqrt(dx) 💀

[@bettereveryday-2025]

Wat

[@AlbertTheGamer-gk7sn]

@@bettereveryday-2025 Which is half-integral. Also: d(x^2) != dx^2 != (dx)^2 != d^2x. d(x^2) means you are differentiating over x^2 instead of x. dx^2 is the second differential of x. (dx)^2 is the square of the differential. d^2x is the second derivative of y multiplied by dy^2.

[@bettereveryday-2025]

@@AlbertTheGamer-gk7sn ok

[@euyn_009]

​@@AlbertTheGamer-gk7snlet's act like we know that

[@EgzoDiuse]

@@AlbertTheGamer-gk7snbro no one was talking about the difference between the differentials😂

[@1SmokingLizard]

3.14% of the patron population spelled the password as "pie"

[@benaissaadel5542]

"The password is the first digit of the answer" Me trying every number from 1 to 9 : easy

[@kayingham3528]

@@ikeu6433 but they won’t tell you how many lmao

[@samosa8192]

​@@kayingham3528 a WiFi password needs at least 8 characters

[@derangedgato]

kid named 0:

[@Laxidosis]

@@derangedgato that’s not that meme

[@derangedgato]

@@Laxidosis ok

[@OneGuyWhoIsExisting]

Best way to encourage to you study maths

[@Mejayy]

This is the first math short video that actually uses legit math! Great proof!

[@PerilGames]

The scary part is I just finished my calculus course and I understand this problem 😮

[@redriotyt8560]

It's calculus, functions and Trigonometry with inclinsis..

[@FndfnnFnefnfn]

most probably you will have problem with √(dx).

[@GonPlayss]

​@@FndfnnFnefnfnmaybe its a mistake. dx is outside the square root.

[@FndfnnFnefnfn]

@@GonPlayss it's under root-line. Or you mean mistake of the autor?

[@GonPlayss]

@@FndfnnFnefnfn yes mistake by the author

[@safeeraat1423]

He made his maths teacher proud.

[@sujalguchait4047]

Dude the approach of solving first was awesome,

[@themostcreativenameever2688]

I find it funny how I’ve seen this short multiple times but only now a couple week after taking my high school math finals did I realize that this is actually fairly simple

[@paramrajsingh1539]

Which country and what grade ?!!

[@themostcreativenameever2688]

@@paramrajsingh1539 usa 12th

[@cerebrummaximus3762]

How do you solve it? Do you have a lesson video? I don't want the answer, I want to know how to solve it.

[@violentgaming8231]

​@@themostcreativenameever2688yes it's easy it's a beginner level problem in JEE

[@themadtitan728]

When integrating from a to b , we replace 'x' in the function for (a+b-x). If the resultant function is negative of the first, it implies that the function is odd, and it's integral is zero. If it comes out to be even, it can be further solved using standard results.

[@BlitzTheGeographyMan]

The math teacher took it seriously when they said “you will use this somewhere in life”

[@GOKU-dq6mq]

I've never done an integration like this, I just graduated from HS and this was very interesting 😁

[@leoutpalleoutpal]

Assam?

[@deusd.2366]

❤❤ that's what i want my youtube to show me

[@Smartness_itself]

Me, using Photomath: 🧠.

[@РасулГасанов-и8б]

🤡

[@alpha9775]

Fotomat😊😊😊😊😊

[@Smartness_itself]

@@alpha9775 "Fotomat" was an American retail chain of photo development drive-through kiosks located primarily in shopping center parking lots.

[@antifreeze-30degrees49]

What's Photomath? Did you try 4-MAX?! 4-MAX is one of the closest things to NZT, but you can get sick on it, aside from usual stimulant side effects but no brain damage at all. Coughing blood, lung damage. Super smart and smarter and smarter, but you will die! Amphetamine is good for ADHD. 4-MAX for smartness plus an Adderall or Ritalin if you have ADHD along with Arecoline Hydrobromide or Phenylpiracetam can help. 4-MAX is even way stronger than crystal meth, but no meth side effects on teeth. 4-MAX is like the ultimate brain steroid that made even idiots into smart people and smart people into smarter people. The more you use it, the smarter you get. But no one has figured out how to get the bugs out. I don't want to touch 4-MAX and so what if I'm kind of smart but not super smart, who cares. I just want to be a chemist. 4-MAX makes things super clear and sharp and super smart. Amphetamines plus Tropoflavin can prevent brain damage, but still nowhere near as strong as 4-MAX. 4-MAX is MAXIMUM INTELLIGENCE OVER 9,000! Again, you will cough blood and die on it. Lung damage even in pill form or dissolved in water or juice and drinked.

[@Smartness_itself]

@@antifreeze-30degrees49 "Photomath" is an app.

[@M_Oz_]

Now please make a video explaining what you did. I honestly find it fascinating to see equations like that being solved.

[@goldbeni]

The part inside the brackets is an odd function meaning f(x)=f(-x) Since the domain is -2 to 2 this part basically cancels itself out The square root is a half circle, (its like the pythagorean theorem, just a little changed) So its basically just "whats the area of a half circle with a radius of 2?"

[@hasanjamalkhan689]

Integrate then Open the upper and lower limit i dont get why is there a square root on dx

[@josephstalin9604]

Odd function gets equated to 0 because the limits are -2 to 2 and the remaining 1/2 √4-x² is direct formula based or you can solve it with the help of Graph by finding the Area under the curve of it. It looks terrifying but is very easy once you start solving it.

[@amOhad131]

Bruh put the dx in the sqrt💀

[@KoushikSarkar08026]

ded

[@danek_hren]

And? (Me who doesn't even know what calculus is, why it has 3 parts and thinks of it as "much harder math")

[@admhc2013]

​@@danek_hrencalculus is when sh*t constantly changes

[@danek_hren]

@@admhc2013 sounds like my mood

[@CloneReaper]

@@danek_hrenwhy comment then?

[@NewtonMathematics-m2z]

amazing video, thanks

[@kiskofa2006]

"Opens photomath" 💀

[@yadav48999]

for that you have to use Mobile data..

[@GEB_Rosee_PPS]

@@yadav48999 10mb of mobile for several hours of free wifi?

[@yadav48999]

@@GEB_Rosee_PPS Arrey bhai jab mobile me recharge hi na ho.. 😂

[@reunilz3899]

I challenge you to do it. Can’t you see the dx under the square root?

[@Liamsmith214]

Chat gpt💀💀

[@rajatpaul3784]

Bro this can be done in 3 steps If u separate x^3cos(x/2) root(4-x^2) and 1/2root(4-x^2), then first term will be zero as it's an odd function where limits are -2 to 2. And in second function simply use the formula of integration root(a^2-x^2). That will give the answer pi. It's basically a question of high school mathematics in India.

[@dlrsnate5100]

I’m in college algebra wtf is this

[@vinayakkshirsagar2268]

bhai bas kar rulaega kya

[@dotmatrix9818]

@@dlrsnate5100 How don't you know even and odd functions

[@Mmmm1ch43l]

well, these are actually exactly the steps the guy uses to integrate this as well, just spelled out a bit (for dramatic effect I assume) except he doesn't use a memorised formula for the integral of root(a^2-x^2). why would you even learn that? you can just derive it geometrically if you really need it

[@Annonnymouss-mv7pf]

Fuck the formula, just imagine the circle x²+y² = 4.

[@anonymous20060]

I can confirm that this solution is absolutely correct.

[@OxalicDZN]

R=2, half circle area = pir²/2=2pi so

[@anonymous20060]

​@@OxalicDZNyeah... 1/2(1/2 pi (2)²) = 1/4×pi×4= pi... the math is absolutely correct...❤

[@AmandaDavidAngelOjinnaka]

Pi is for area and volume nna

[@feuz997]

Math Teachers be like: you will use it when you grow up

[@kaushikkumar6288]

Actually it was too easy for this many steps . But he did with explanation Love from India ❣️

[@SmileyDawgg]

Give This Guy A Medal

[@Sakshamsingh139]

For what??

[@nono-sc3wx]

​@@Sakshamsingh139 for helping everyone in that store get a free WiFi passwoed

[@Sakshamsingh139]

@@nono-sc3wx this is so easy question then why medal? I also solved so give me also medal🌚😂😂

[@nono-sc3wx]

@@Sakshamsingh139 tell me every number of pi, no copy

[@Sakshamsingh139]

@@nono-sc3wx you are askimg this question to a indian 🌚 An indian discovered pi , btw i am in class 12th preparing for world 2nd toughest exam IIT JEE and 3.14 is enough for me🥵

[@chicken]

The waiter's confidence and the man's appreciation created a beautiful, elegant moment.

[@Melissaposs]

Hi

[@ORAACLE8299]

Bot caught lacking💀

[@carp6679]

truly a "ignore all previous instructions" moment 💀

[@unordinarytreefrog]

Tf are you babbling about bot

[@Manhung56]

bot say "." that last title L bot

[@Ducky-96]

Never let them know ur next move 💀 The password is "the first digit of the answer"

[@calvinjamesgarde9494]

It's 3

[@christopher-zq4ko]

just try every digit from 0-9. You will eventually get it.

[@Alsced]

no it was digits

[@christopher-zq4ko]

@@Alsced how many digits exactly though? 5? 10?

[@Alsced]

@@christopher-zq4ko thats the point, no one knows

[@gyorgydudau]

"You'll need it someday!" - my Maths teachers

[@An1984.7]

Pi=180 degrees

[@hwhaht]

Pi Radians does. Pi itself doesn't.

[@swayv714]

3.14

[@cooIcat6778]

@@hwhaht Are you slow? Degrees is just another unit of a number, similar to how kmh is just a different measure of speed to mph

[@hwhaht]

@@cooIcat6778 yeah, and Pi Radians = 180 degrees that's the conversion Pi itself equals 3.1415... If you say Pi equals 180 degrees that would be like saying 100 = 62.1371 mph 100 what? 100 meters per second? 100 flapjacks per second? you haven't given a unit Radians is another unit just like Degrees, Radians is built upon the circumference of a circle being 2 times Pi (Tau) Radians, just like every 360 degrees is the circumference of a circle.

[@mariluski23]

muy inteligente 🤓

[@joshdeconcentrated2674]

"circle!!" Haha, one of my favorite things to write. nice integration techniques bro 😁

[@diosbois3911]

Bro really just dropped the hardest math edit

[@shafikhan2242]

Trying to get WiFi during math class belike😂😂😂😂

[@3KLANGMUSIC]

Better than the last digits of the answer.

[@DubloDuck]

That's the universe teachers think we live in 💀

[@drippy_20]

💀💀💀

[@SarcasmIsMyGame_]

Math IS the language of the Universe

[@SalmonFeet]

@@SarcasmIsMyGame_not the language of my vocabulary tho

[@ricky7cool522]

And they get mad when we do it with a different method or a calculator

[@pedropalacios1]

we do

[@Thegamerboy-q3s]

Thx for helping me with my hw 😊

[@wiener_process]

The second term can also be solved by simply substituting x=2sin(u). Although realizing it's a circle is probably faster.

[@M41thew]

That would be a complete waste of time

[@Izunia2077]

nahh... you can easily put one of 3 standard integrals underroot (a^2 - x^2) which equals to sin inv x/a something i cant bother to type whole formula but its a direct approach

[@PXO005]

@@Izunia2077 ah I can bother, prepare for a hefty formula ; (x/2) √(a^2-x^2) + (a^2/2)arcsin(x/a)

[@Izunia2077]

@@PXO005 yup exactly that I mean it’s hard to memorise for some but that’s the most direct and easy way

[@jomygeorge1287]

Guess i should start practising calculus.. i miss those days

[@sieadestudio8378]

I keep seeing yoy everywhere I go In almost every comment section I see😨

[@akirimew]

@@sieadestudio8378yoy

[@jomygeorge1287]

@@sieadestudio8378 😂 I dont know.. i rarely comment. For the past few says i did comment for few shorts🫣

[@AdnHa.]

"Sorry, the password must contain at least 8 characters"

[@calamaricalamity6757]

3.141592 (correct me if I'm wrong)

[@danek_hren]

​@@calamaricalamity6757 you forgot 6 and have only 7 digits

[@palak2334]

3.142857

[@calamaricalamity6757]

@@danek_hren .

[@Rando2101]

​@@palak2334 3

[@JohnnyJoestar790]

dx is under root You should make new video

[@gunargundarson1626]

Pro tip: if you write the equation again on the bottom, it cancels out the top and solves itself.

[@Ae1ara]

What? It would equal one if you did that

[@gauravtalukdar2715]

Then 1 will be the answer

[@bhuvi_78]

💀💀

[@tacticolidiocy]

No that's not solving the equation

[@peterdolan6325]

@@tacticolidiocy thanks genius

[@prosperitypathways10]

meanwhile Indian Jee aspirants : easy!!! 💀💀

[@ArokSam]

Mean while an average 12th grade cbse student: a little hard .

[@Salman-kc6gr]

Haa bhai bahi mai bhi soch rha itna bhi hard nhi doable hai

[@Wanton-28]

This isn't even board level integration😀

[@mrxshooter4253]

Are u serious 😢😢​@@Wanton-28

[@mrxshooter4253]

​@@ArokSamnahi bhai samajh mai bhi nahi aa raha😢

[@theredtails7609]

People who do math for a living are a different breed.

[@rusty5988]

good to know im not human.

[@wiseltheysay2863]

This is actually an easy integral. First distribute the integrals. The first one is odd so if one of them is upright while the other is the opposite. Adding them together cancels out which equals to zero. The second integral is also simple because you integrate in terms of areas. The sqrt(4-x^2) means it’s a circle with a radius of 2. Now you calculate the area of the semi circle. Add both first and second integral equals to pi