Beautiful JEE Advanced Problem From IIT Professor Notes

[@Ajay_Vector]

Another solution : I done this by putting lnx = t And got an ODD FUNCTION within the limits -infinity to +infinity and thus this comes out to be '0' .

[@vedant3148]

I also do same thing

[@Unique_India..]

I am in 11 and done in first attempt

[@being_1]

But that is approcahble because infinity is not fixed And rimmann's paradox also comes in bro you have wait for the result.

[@Ajay_Vector]

@@being_1 In this question, There is also Infinity then why sir not use riemann paradox

[@AkshayKumar-sw5kp]

​@@Unique_India.. beta chu** kisi aur ko banaana😂😂

[@28aminoacids]

Here's my thought process on how you yourself can come up with the substitution x=1/t: First, you have to be able to guess the answer must be zero. Putting ln(x)=t gives you an odd function with limit -infinity to infinity. So you know it's going to be zero. That means some part of the integration is negative and some are positive. You think and you see ln(x) is negative for 0 to 1 domain. That means if you break the integration into two parts: from 0 to 1 and then from 1 to infinity, you get zero. So now you think what substitution will change the limits from being 1 to infinity to being 0 to 1. There you have it. x=1/t does the trick. It takes what's inside 0 to 1 region to the outside and whatever's outside gets right back in. That's why x=1/t works like a magic.

[@nishansarma660]

I think sir is doing wrong, first he flipped the limit which gives a - sign then the other - sign before 1/t² should be multiplied and I should be equal to I

[@abhirupkundu2778]

@@nishansarma660 he did not flip the limit. After the substitution, the limits change, check carefully. Then he flips the limit.

[@GSanjawad]

Another solutions 1. Put tan-1(x) = t i.e. tan(t) = x and apply king's rule and done 2. put 1/(1+x²) = t and you will find simple integrations of log 3. Put logx = t and you will find odd function .

[@mrinrajmandal6556]

What is king's rule

[@harshsrivastava9570]

@@mrinrajmandal6556 watch some videos, they explain it beautifully

[@mrinrajmandal6556]

@@harshsrivastava9570 Give me the video link

[@DhruvGandhi2005]

another solution is to use IBP assume logx as 1st function and x/((1+x^2)^2) as 2nd function and then apply IBP

[@DhruvGandhi2005]

@@mrinrajmandal6556 integral xdx(0->1) can also be written as:integral (1-x)dx this is King's rule General form: integral xdx(a->b)=integral (a+b-x)dx(a->b)

[@pallavimanav3745]

IIT IS LITERALLY A BRAND AND PROFESSORS ARE ALSO ultra GENIUS

[@bhargavsai8014]

​@@priyangsudas5167 rankings depend on a lot of different factors tho,and IIT Bombay and Delhi are in 170's btw

[@saswatasaha9519]

The professors are not just genius but savagely genius

[@nevergonnagiveyouupnevergo5907]

Bro IIT professors are great researchers but not great teachers

[@thetemplest5856]

Brainwashed Indian be like

[@kunaldas9543]

​@Raj Chaudhary wp university ❤

[@parveshbansal9175]

Yes sir please upload more questions from these sheets.... It is really very helpful

[@aadi7529]

A more beautiful question would be |\int \limits_0^inf x lnx dx /(1+x^2)^2| basically mod of the function

[@snow5064]

another method is to solve by substituting x=tan t, and then doing by parts. though the limits there require a bit of thinking as they are infinity-infinity type but eventually the ans is 0. although sirs solution is definitely more elegant

[@ankitasomani2460]

the way i did it : take x² common from the squared term in the denominator subs 1 + 1/x² = u convt the log term in that form then apply IBP and there you go :)

[@hustle241]

GREAT APPROCH.

[@dipyanshukumar3459]

Here's another solution to this ques... just put x = tan theta eventually by using kings rule at the end u will come up with log 1 which is actually 0 so integral becomes 0

[@Harsh-hr1yq]

Gem of mathematics

[@kattariitian]

we can put log x equal t and then limits will be from minus infinity to infinity then apply kings rule hence it will be zero

[@yogesh8154]

I got this question correct in my first try Actually when we have limits like x to 1/x we should use this substitution I got this observation from an mock test

[@lbwshorts6716]

Another observation especially in "DEFINITE" integration may be ki agar x ke saath log ka function rahe then also we should go by x--> 1/x substitution.

[@snow5064]

it is useful often but not always, sometimes x=tant is the only way to go specially in situations like integration of logx/quadratic,(the limits are 0to infinity)

[@goutamboppana961]

or can we think of it this way, like as we put 1,2,3, and so on the value approaches 0 so the total value is 0? or am i wrong?

[@MohitKumar-bh9mx]

My solution- Let x=tany ⇒ dx=sec²y dy. also denominator=1+x²=1+tan²y=sec²y. Now put this back into the integration and simplify, you'll observe it becomes ∫(siny)(cosy)ln(tanx)(from 0 to π/2)=I(let). Apply kings rule so I=(cosy)(siny)ln(cotx). add both the integral and you'll observe 2I=0 hence I=0

[@evergreenmelodies4610]

*Upload Chapterwise Topicwise Analysis of Mathematics JEE Advanced-2009 & 2016 Conducted by IIT Guwahati for JEE Advanced-2023.*

[@palashpaiangle6894]

Can solve it as an indefinite integral as well using method of parts Put( x/1+x^2)=dv/dx so v=-1/2(1+x^2) And take lnx=u Final integral can be solved using partial fractions

[@DhruvGandhi2005]

I also did the same thing

[@allukachallu154]

By parts then partial fraction and got this by putting limits You get( - ♾ /2 )+( ♾) - (♾/4) - ♾/2 - ♾/4 ---------> - ♾ Finally - ♾ + ♾ -------> zero 😁🤣🤣 Edit 1 : I solved it like this too, but man I seriously don't know if this is correct approach or not🤣🤣🤣🤣 Edit 2: best approach for such questions is substitute T ratios , like substitute x = tan theta here.

[@sleazyuchiha4625]

Another method can be Laplace transformation by multiplying e^-bx and then differentiating wrt tob to form a function wrt b Edit: For anyone wondering where I got it from , go and see Kundan sir(PW) lecture from last year Prahar batch he has explained Laplace transformation there and how to use it in integration where limits are from 0 to ∞

[@abhinavrawat6632]

Thanks for telling bro

[@AryanSingh-xx4py]

Literally i am saying this is one of the pyqs of advance paper I do not able to solve and after that I quite studying maths from that time really thankful to Aman sir ❤

[@spandanpatil5746]

Substitute X as Tan and then you get a step of integration of log tan which is zero over o to pi/2 so final answer is zero..!!👍

[@diskritis2076]

This becomes very easy if you use feynmans trick. just assume I(t)=x ln(tx)/(1+x^2)^2 and differentiate and then evaluate an easy integral to get I'(t)=1/2t. Then we can easily say that I(1)=0

[@abbashussain6419]

Correct in 1st try.bring more questions like this sir

[@RNR_2k6]

Thanks a lot, sir, for uploading such amazing questions🙏🙏.......I solved this question by assuming x²=t and later it becomes " Integral by part" and got the same answer that u got.🙂🙂

[@BlackScreen_Singer]

You should make a video on what does matrice multiplication and matrice algebra physically represent. And what is the physical world meaning of determinants. I have seen many lectures but no one ever told me the physical meaning ,all they did was show how multiplication is done or how value of determinant is found. Same goes for most parts of calculus as well

[@nilanjanpradhan1385]

Look for some data science lectures you'll get to know

[@varunarora1256]

You should check out 3blue1brown essence of linear algebra series

[@harryminati9685]

already done in class by ashish aggarwal sir and he also taught us to try this substitution that in 90percent cases this substituion works where limits are reciprocal of each other

[@jayeshvaripatil5139]

Amother method is putting x= tan0 and then you will get Sino.cos0.ln(tan0) from 0 to pi/2 Then apply king property younwill get cos0 sin0.ln(cot0). From 0 to pi/2 add both sin0.cos0 will be common the. Ln(tan0)+ln(cot0) will be zero

[@shresthshankhdhar375]

Ha chahiye aise question

[@dhruvbhatia6808]

Sir I I have another solution for this If we substitute x for tan theta we will be able to convert the limit from 0 to pi/2 thereby allowing us to use the properties of definite integration After subsitutiing tan theta apply integral = sum of a+b-x integral and we get ln 1 in our integral when we add both hence getting 0

[@Pramod_pippal]

My solution : let 1+x^2 = t , xdx = dt/2 and then solving by parts , we get t^3 /t-1 solving by partial fraction and finaly we get simple integration of 1/t-1 and we get our answer by putting limits.

[@danishshaikh2490]

Another method is put x as tan t and then apply a+b-x

[@dineshshriramwar7488]

Another way could be: take logx as 1 and x/(1+x2)^2 as 2nd function and then byparts 😊 easily I got its ans

[@11__11__]

Same

[@dineshshriramwar7488]

@@11__11__ but we will get problem at last step

[@adityamanohar2564]

Limit fasegi bhai

[@SPclasses997]

Nice 👍

[@atharvamhaske30]

Baiscally it's a thing that I have had know from chapter limits as in inf - inf we try to put x-->1/t so it's very standard approach as limits get interchange and get back again to same intergal or limit

[@kushagrakatarexi-arn682]

SIR PLEASE BRING MORE SUCH PROBLEMS however I did this in my first attempt by simply integrating with BY PARTS AND applying limits at the end ❤❤❤❤❤❤❤❤❤❤❤

[@vanshajverma2199]

Same approach by me too👍

[@kushagrakatarexi-arn682]

@@vanshajverma2199 👍🏻👍🏻

[@RaajYadav-ms6ri]

Thanks sir ❤❤❤

[@excellentgaming611]

Aur questions pe video

[@kunaludakhe8672]

Log(1/t) is -logt and there already -1/t^2 dt is there so it will be positive ( negative * negative = positive)

[@khushbu9400]

Alt Put x=tanb And then apply queen rule (making limit half) Just 2 lines

[@RakeshKumar-rc4sj]

Easy method is to use (x^2+1)=t and then substitute t=1/z ....you will directly get0

[@seemamittal3677]

Please bring more kind of problem like this from these notes

[@dhruv6342]

Take 'x' out from bracket and just put logx=t

[@vedant3148]

Sir how will you take "-ve" sign after interchange limit of integral 0♾️ in presence of -[(1/t) square]

[@sanidhyamaurya8909]

Legend guessed the answer would be 0 by simply applying the basic concepts of limits

[@subhrayanbarman1654]

Let's denote given integral by I, then- I= int(0to∞) xlnx/(1+x²)²dx Let, x=1/t =>dx -1/t² dt I=int(0to∞) -tlnt/(1+t²) dt = -I => I =0

[@a.dlegendary7978]

Yes sir aur sawal liya

[@Akhil-ms1qx]

another solution x = tanx then apply integral 0 to 2a property then the sum is zero [ f(x) + f(2a-x) = 0]

[@impresent2005]

Yes sir we want more questions💕💕 Becoz Maths is not a subject it's a limitless food for a hungry man✌

[@impresent2005]

Love form Hindustan 💕

[@Batmanpk6_ps]

​@@impresent2005 to hum Kahan se hain bhai😅😅

[@dumbwit662]

Wow sir question dekhte hi pura solution mind me aa gaya ek jagah atak gaya but ho gya Masst question tha aur questions aise laiye please

[@shreyanshverma7345]

Sir plzzz in assignments ke aur ques laiye ya inka link de dijiye plzzzzz

[@rj18-cz8em]

Yes sir more questions like this😊😊😊

[@nish7009]

i used a very basic approach in my solution, i took 1+x^2=t, seeing that i already have an x in the numerator and thus it is an easy substituion, after which i get 1/2*integration from 1 to inf of log(sqrt(t-1))/t^2 dt you can then use the property of log take out the sqrt, after that take t common inside the log, i did this because i can see that integrating logt/t^2 is easy with by parts and that after substituting 1-1/t=u i get a very easy integral. i calculated both separately to get -1 as the answer for log(1-1/t)/t^2 and +1 as the answer for logt/t^2 which overall gives you 0

[@adityamanohar2564]

Ese aur sawal late rahiye sir 😊

[@akashkumargope1044]

It's simple question 😂; put X = tan a . And logX = log tan a =0 then answer is 0. Solve it 👌

[@pawanmathmatics]

Can be done by simply substitute x as tan(theta) ,change limit and use kings rile

[@ujjwalghosh389]

Sir please bsc maths ki bhi class ap start karyaye na....🥺🥺🥺🙏🏻🙏🏻🙏🏻🙏🏻 Sir please please please 🥺🥺🙏🏻🙏🏻

[@preethamjee6022]

A similar question was given in Putnam Olympaid 2005. This can also be solved using Feynman's Technique.

[@advaykumar9726]

Can you explain how?

[@aditsaini5094]

Brother feynman technique jee me padhate hai kya ya meri coaching ne hi nahi padhaya

[@preethamjee6022]

@@aditsaini5094 neither did in our institute. I've self learnt stuff

[@preethamjee6022]

@@advaykumar9726 Take I(α)

[@devyt23]

sir please provide pdf of these questions

[@ranjna7289]

me who is in 10th - limit tending infinity dividing something by infinity is zero thus this integral equal zero i am actually in 10th but i like calculus and this question took me 5 seconds to solve

[@vinitchaudhari9534]

SIR PLEASE MAKE A JEE ADV 2023 SELECTED PROBLEM PRACTICE SERIES FOR MATHEMATICS🙏🙏🙏🙏

[@lbwshorts6716]

Substituting 'x' as tan(t) makes it really easy and proceeding by King's Property !

[@Princ70]

Same approach Last me ln1 bna hoga Which is zero

[@vaibhavporwal8539]

Sir please provide all the questions from those sheets 🙏 .

[@devyt23]

sir aesa question jee main 2022 mein bhi aya tha (same approach wala)

[@avimathur6822]

Sir how dx become= 1/t².dt

[@Samphysicsguy]

this question can also be solved taking no 1 /( 1 + x2)=t remember that u have to use one of the properties of integration to get the final answer

[@deepsirsat8076]

Add some more questions sir please..

[@shortmakers5336]

Sir please make next video on maxima and minima. video was quite interesting

[@aditya_sharma__10]

Another method: substitute x=tan(theta) and apply properties and finally +I -I form will come and the and will be zero

[@atridevbhattacharya5050]

sir solved it

[@Dk-hd1sj]

Jod or wot

[@atridevbhattacharya5050]

@@Dk-hd1sj meaning

[@Dk-hd1sj]

@@atridevbhattacharya5050 bro it is a phrase used to show expressions like ' wah bhai kamaal krdiya'

[@swastikabanerjee2545]

​@@Dk-hd1sj bro it's easy if you substitute it with tantheta and then use property of integration

[@NTAunofficialGOV]

Sir plzz BRING SESSIONS ON mathematics of class 11-12th being applied in real life

[@arpittiwari3541]

These are literally the simplest integrals, whenever you see the integral where their limits are reciprocals of eac other your substitute x as one over t.

[@lizapatel7055]

In integration, When any method doesn't apply and limits are reciprocal then put x=1/t and start

[@GoodDaysOP]

Thanks mem

[@lizapatel7055]

@@GoodDaysOP our sir said once 😅

[@riteshmishra6800]

Sir pllz tell us bansal classes ki sheet ki konsi exercise ka q h

[@vinayak9828]

Very easy problem jee mains level 👌 Same concept problem was asked in jee mains 2023 January attempt 29 Jan shift 2 paper

[@theepicman8160]

Sir you are my favorite teacher of this beautiful subject mathematics.

[@debojyotisaha6189]

Sir please bring a series for this

[@shrawon3605]

Very easy question

[@siddharthadityak965]

sir we require more sums like this. plss make or share such assignments.This would be more helpful

[@chenehsagar6348]

Sir can you give all the questions of these assigbments

[@mr...........4921]

another approach we can also do 1/(1+x^2) = t 🙏

[@sbanerjee1338]

ans 0 hai. Solved verbally by substituting x = tanθ

[@piasdas0582]

It was a lovely 🌹 math. We want more like this sir. Love from Bangladesh

[@Omm00033]

Class 12 jee ke preparation ke liye kon sa book le sir plese bata dijiye 🙏🙏🙏🙏🙏🙏🙏🙏🙏😭😭😭😭😭

[@rohitKumar-gu7dc]

Please or question v laaiyega

[@warriordefenderw_d6614]

Mine gone little long but got 0 finally 😅😅

[@depressedguy9467]

Me using contour integration

[@Anonymous-lw5lw]

i did trig substitution and it worked

[@technicalworld7714]

Sir please give the full assignment 🙏🙏🙏

[@Caffine55]

Same question karwaya tha GB sir ne class mai ...!

[@abhishektripathi6600]

This could also be done using integration of ODD FUNCTION!!!

[@ayushrajput6354]

Bhai limit dekho x€ (0, infinite) X does not belong to -R

[@shivamsinha8540]

Sir if we put logx = t and then put the limits in logx then new limit is infinite to infinity and we know that two same limits integral gives value 0 Is this also right approach?

[@bhupeshverma6489]

Sir kuch aur questions practice karva dijiye na sir assignment se sir

[@shantanupradhan3086]

Sir i want these assignments pdf Can you please provide Especially the pdf of sheets of bansal sir

[@programmingwithkartik4319]

sir ek dedicate question laye log and its properties pe

[@namantenguriya]

Rich content ❤

[@hpthemagical]

Sir please Give us the complete notes

[@shivamraj5391]

Sir aur karwa dijae is assignment mai sai sir

[@ronak3990]

❤❤❤

[@nointernet-hr]

Interchange krne ke baad negative sign kese aya 🤔????

[@aranganathansubramanian1141]

another method: put (i+u square ) = u ..u might get some numbers like ln(0) , or ln (infinity) ..but it will be cancelled by another such term. Pls crct me if i am wrong

[@aritrabarman8763]

OP q sir.....sir woh assignments telegram pe bhi de dijiye na hamara bhi bhala ho jaye

[@pravinabhansali9541]

Can also sub x = tan y Then use king and add