Monster Question of Integration... 

I have searched the entire yt but only this video has broken the que down into its basics . .... this video is a life saviour

Ek approach ye bhi ho skti h ki hum pehle wala concept use kre jo apne limit of sum ke do concepts explain kre usme se. Pehle wale concept ko use krne ke liye pehle hum dono taraf log lenge, x/n ko niche utarenge, x ko limit ke bahar lejayenge as a constant, fir hum product me r/n ko extract krenge (n^n se divide krna h numerator aur denominator me, (n!/n^n) to sidha r/n ban jayega, fir (x + n/r) /(x²+n²/r²) me hume r/n se upar niche multiply krna h , n!/n^n se jo r/n extract kiya tha usko hume denominator me multiply krna h, fir log ki property se product ko sum me convert krenge. Ye sab krne ke baad sigma ki general term banegi : log (x(r/n) +1)/(x²(r/n)²+1). Ab to bas hume x ko integral ke andar constant ki tarah treat krna hoga aur simply 1/n ko dt aur r/n ko t put krna h. Fir hume integral milega: x ∫ ln(xt+1)/(x²t²+1)dt with limits from 0 to 1. Ab hume xt = u substitute krna h aur x dt = du rkhna h. Finally integral banega : ∫ ln(u+1)/(u²+1)du. Aage to same h. Pin krdo sir ji bhot mehnat lagi h 😢 Edit: aakhri integral me limits from 0 to x hongi of course.

I m 60 years old, attempted IIT too, still crazy about what you have just explained. Your intensity, great.

How wonderfully he solved this problem.... even after forgetting those things for years now... I could understand the solution in its entirety....massive respect. God bless u!! ❤❤

Probably,the toughest question ever asked and one of the most interesting question

until last year i used to watch your channel now i am watching it while sitting at my room in IIT😎

I'm currently a student in one of the NITs, in my 3rd year, but still seeing the question and watching Sir solve it felt surreal, sent me back to my JEE prep days and awakened a lot of memories ❤.

*1% means almost 2000-3000 students were able to solve this question. This is disturbing because India is soo much Overpopulated country that number of toppers in our country is far greater than number of average students in other countries. The competition is so intense, no doubt many students suffer depression because even after working soo hard, they don't make it due to limited opportunities.* *In India, you have to work extremely hard to achieve a even a normal thing and you don't even get half of what you deserve. All the blame goes to the 1970-2005 generation people who kept having kids despite of their poor financial condition. In 1970, population of India was 60 crores but in just a span of 40-50 years, the population grew to 140 crores. More people with limited resources means more competition. People have done so much for this country, many people even gave their lives for this country, but all this country gave back is poverty, unemployment and extreme competition.* *A forced implementation of one-child policy is the only key to keep this country sustained, or India is doomed. A civil War is much likely to happen due to lack of resources and almost unlimited people to consume. The so called "Survival of the fittest" is near.*

Me watching in my 3rd year. JEE Advanced questions always ask my inner conscience to explore about

sources say that jishant nindal was among those 1% students who could solve this question during exam

jee 2016 was of monstrous level Physics had 2 mind blasting questions based on corealis force and precession motion

Dude our sir solve it in 1 min and we can too.hatts off to one and only Goat Ashish Agarwal sir

I wish you were a teacher in my time when I was preparing for JEE. I surely would’ve cracked advance. You have made the question so easy by teaching basics so well that even an average kid can understand this.

Right now in IIT Indore 4th yr....cannot believe we used to do these type of questions during our preparation years...right now it feels next to impossible for me to even approach JEE advanced questions which we used to do easily back in those days

This has to be the peak of calculus if anything. Probably the greatest thing I’ve ever seen.

Hats off to that students Jinhone tukka Mara hoga aur answer correct❤❤😂😂😂

Cant even imagine solving these type of questions in such crunch times during exams !! you literally need to be perfect in everything 🥲

This can be solved easily. 1. Designate x/n as “a” 2. Transform to eliminate n! and n^n 3. Take ln on both side You will get terms like a*ln(1+a/1+ a^2) + a*ln(1+2a/1+4a^2) … 4. Differentiate and since a is tending towards zero. The term remaining would be ln(1+a/1+ a^2) + ln(1+2a/1+4a^2) … 5. Now we know for each a>1 ln and in turn f’x would be surely negative solving option 3 and 4 6. For a

IIT Guwahati supremacy>>>>>>>>>>>♾️🤐😶😱😱

Any one noticed in which year this question appeared.2016. JEE ADVANCED most difficult paper in History.

I tried but I failed to do so now I'm Peacefully living in my village and watching this😂

Bruh I'm telling the truth the people who crack IIT with very high scores,most of them have knowledge of this type of problem from higher studies,or (advanced study),I will recommend the Engineering mathematics book(B.S Grewal),if you do some particular part of the book,then you will understand what type of question the professors make,it seems like they show extreme creativity when crafting a question,but the truth is if you have advanced knowledge,those creativity even doesn't give you a sweat,,you can creack many questions easily,and trust me there are so many shortcuts you will learn from the book,that requires very much calculation from the perspective of a 11-12 standard student.

☠️☠️Salute to those 1.04% brilliant minds 🤯🧠>>>>>>>>>>>>>♾️♾️

I am 31, but still amazed that i tried JEE, it looks so difficult but when now I see it looks like a poem, just need passion to solve

Me being in class 10 (2024-25. Batch ) not understanding a single thing and all the things he said is going above from my head , I have plans to take PCM after boards but seeing this....Calculus is tough....💔

Actually question easy Hai but conceptually deep that's why during exam it take lot of courage to get into question like this. I'm also among the one Who solved this question.

Great video, JEE Nexus! I really appreciate the way you break down complex concepts into bite-sized pieces. Your teaching style is so clear and easy to follow. Keep up the good work! #LearningMadeEasy

Rankers are not those who solve these questions rankers are those who dont even waste single second in these questions and move onto next . . . . Obviously 1-100 rankers are exceptions

fact is that these questions are greatly inspired by some hard to find old books of college level Maths

Just wow!!!!!! Aaj hi hmare yhan definite integration ka second lecture tha and mai dinner ke baad idhr aaya....coz integration kaafi dekh hi chuka tha toh yeh video bhi dekha and kasam se mza aa gya sir

Samaj aagaya bhai I m from nepal and I m not preparing for IIT too still I got it it proves how well you explain I like your lectures so I watch it bahut hi mast question tha❤

I am in 12th studying integeration and ise dekh ke toh 😂😂

i solved this question(by my own) and literally it took me 15 minutes to solve the question completely how were those 1% students who have solved it in 5 minutes(hats off to them)

Nicely explained bhaii... Itna effortlessly bta diya itna khatarnak question... Poora smjh aya dhanyawad

Brain Storming 🤯. Teaching style is so good.

OP question sir! Maza aa gaya. Ab aur mehnat karni padegi ❤❤

Ashish Agarwal sir is a gem... He explained this qn in class❤❤

Looking at it now after settling down in life, I think this level of problem solving skills should instead be used for an entrance exam for a job in ISRO or a real world problem solving competition of some kind rather than for an entrance in an engineering college of a country not known for any engineering marvel in recent history!

Not too shabby,good job brother.

This videos give us a courage to change😅

I'm in class 10 but the Thumbnail and the title of the video got me here unbelievable efforts by the teacher and students who attempts these kind of que. Hats off 🙌

Use limit formula for infinite case donot use integration then its so simple to figure out logf(x) = x^2/2-x^3/3

This was the question of my set in 2016 belive me this is question is the symbol of beauty of iit paper ....or may be toughest in the history of jee advanced in maths ...😊

Easy ques tha ye toh, bass exam pressure me solve karna badi baat hai, ghar baithke karna ho tab toh easy hai

The crux of this question is the concept of lim x->inf. And manipulation with knowledge of logarithms!!!! Such a beautiful question!!! 🤩 🔥

Don't overhype the exam mister.....It's not necessary or important or feasible to attempt all questions......why not put these kind of questions in the bin during exam......the topper may not have even attempted this question......some questions are meant to spoil your time and mental peace during the exam....... it's always wiser to leave such questions and even then you can top the exam......... Once you get selected You'll have your entire life to attempt these questions and solve them successfully to get mental happiness about your greater brain capabilities 😂😂😂.....

Ashish Aggarwal sir be like kya hai questions me😂

This question took me complete 1 hour but i solved it completely

EVERY QUESTION LOOKS EASY ONCE WE SEE ANSWER SOLVING VIDEOS😂😂

Me watching this vedio being in 10 class

They could have made a bit more tough if they replaced (x + n/n) and (x²+n²/n²) by x+1 and x²+1 but they chose not to 😅

excellent video, understood the concept completely!!

ha bhai samaj mai aa gaya. more questions like this plz.

Thank you so much sir!!! Iss question ne dimag ke sare concepts chamka diye!!!!!😊😊😊

Really, a beauty! A very explained. Thanks a lot.

close to 100k , lets gooooo!!

Sir I am in class 11.I don't know how to do integration but I understood this question because of your explanation.

Me as a NEET aspirant ☠️

I am in class 11 and just come to see how tough questions can come in advanced

I feel that keeping temperament of attempting such kind of question with accuracy is very difficult task in exam. And sir thank you for superb solution and I am too fascinated by your interest towards explanation of this solution

#iitjee#, please posts sums like these, these are so nice to solve.

Wo sab to theek he sir lekin aapne itna badhiya samjhaya ki ye to tough hi nahi laga aap sachme great ho sir❤️‍🔥❤️‍🔥❤️‍🔥

Literal goosebumps ☠️

Jindal ke paper ka question tha usse puchna yeh hua usse😂😂😂

I aolve this question in 20 min without seeing the solution after solving i checked the solution and ans is correct

bhayankar question. aman bansal macha diya

Thank you sir 🙏

Unique solution ❤❤❤

This is a question of sequence of real numbers actually, mixed with integration.

Beauty of JEE

nishant jindal prob 1 of those who did it in exam

Guys Am taking up the challenge of Best JEE prep Am in 11th For 75 days Targets which are must : 1.solve atleast 15-20 ques per subj 2. 1 hour revision properly with full focus 3.20 min inorganic 4. Cover lectures 2-3 5.Tests every week with proper preparation 6. Excersise atleast 20 min 7.minimize junk 8.prioritize prayer imp... Guys I'll update every day.. This is a challenge to stay disciplined that's it so pl encourage up...

Being a neet aspirant I felt like ki.. ye kya ho rha hai bhai, Bhai mujhe cockroach bana do 😂

I don't think so it's monster it like if u know basics toh hojata .... main reason for less correct and attempt percent is that students thought hard hai lets leave it ... other wise this simplification should not take more than 6-7 mina

We can use stirlings approximation it will make it a bit easier

अति बुद्धिमत्ता परीक्षण का अवसर।धन्यवाद।

I think this question is a must solvable question

thanks to aashish sir we did these type of question in class so its not that difficult for me only the manupulating part is there !!!

If we have fx as a very slowly increasing/decreasing function, we should be able aggregate an approximate value for integral fxdx, by sumation of such areas of n rectangles, where bigger the n, more accurate the approximation...

Most sweet teacher spoted

Guys.. Repeat at least 5 times at 0:38

@blackpenredpen you should have a look at this video. The language might be a problem to you, but the question is of great concept and understanding. I would like to see your take on this.

Sir thank you very much i tried this question multiple times but unable to solve but after seeing your solution,,, me like aur mehenat ki jarurat hai ......

Acculy me exam ke time es type very hard questions chodna hota hai . Nahi to yahi tum ko khayega. Pahala galat hua to negetive, sahi hua to time loss bahat yada. Jo easy easy ( easy matlab halwa mat samjhna , easy matlab jo karne layak questions ho time ke sath 40-50% ) karne see achha rank aa jata hai . 40-50% karnw layak questions bhi kaha milte hai washe 😢 .

Jawab to samajh aa gaya itna clear samjhaya hi hai lekin is tarah ka sawal banatey kaisey hai ..... Unko pehley se pata hai options kya rakhna hai aur 4 me se kaun do options sahi hongey aur baki ke galat Yeh sahi aur galat options honey ke liye f(x) ke liye kaisa algebraic expression hoga jisko ki Lt ke form me rakhey ..... Examinee ko itni samajh hogi ke simply expression me x ki value dalkur to sahi galat options nahi pata kur saktey...... Is Lt ke form valey algebraic xpression ko definite integral ke form me simplify kurna hoga .... Simplified xpression me value put kurne pur sahi aur galat options obvious ho jayengey Video dekhkur samajhna aur khud se exam conditions me sahi solve kurna dimag se bahur ki bat hai Sawal bananey vale se zyada kathin kam lugta hai is paheli ko khud se samajh kur exam pressure me solve kurna I guess To solve such questions successfully during exam i think th student should hav th ability 2 get into th mind of th question setter

I understood everything !!

Watching this video again at 12:22 f(t) is ln(t+1) ok For finding th botom and top limits of integration interval Th xpression of ((rx/n)+ 1)) at r=1 and n tends to infinity is 1 and not 0 That is th botom Lt is 1 instead of 0 and Similarly th xpression ((rx/n)+1) at r=n and n tends to infinity is x+1 and not x That is th top limit is x+1 and not x Somebody let me know if i am wrong because iam missing something

Not so tough. Converting sum to integration is in 12th boards only. Only thing is to check the options smartly.

Samaj kuxh nai aaya but maza aaya 😅

😮 sir aise aur bhi questions chahiye

Nice! 👍🏻

Over Hype kar diya iss question ko

Very beautiful sum😊

we need more!!

Not that difficult to be honest, assuming you know product limits can be converted into sum limits and then to an integral

Sir, bohot khub. Lekin, examiners bachho ko kya Newton, Ramanujan yah Einstein samajhte hai??

I can bet that the 1 percent that solve this question are from fiitjee becoz we have 2 dpp for limit as a sum and they have more tough question then this

Nishant jindal must have solved this one 🤌

I was solving ncert ch 7 integral miscellaneous and this video recommended inspite integral of sum is reduce this year and i am not preparing for iit but i understand this question totally bcz u explained really well❤️❤️

AIR 1-100, left this question as soon as they saw it. The ones who solved it did not get into IITs because by the time they finished it, only 5 min were remaining to finish the exam... Kabhi kabhi jeevan mein intelligent nahin, smart bano, Sprite piyo.....