Possible vs Reasonable

[@dieuwer5370]

Solving a math problem is one thing, but inventing a math problem that elegantly solves to a nice integer is even more fantastic.

[@nickhill6036]

It's been almost 3 decades and a lifetime since I took my jee. Now I am back watching these videos and relearning all of it again. But this it's just for fun. Thank you!

[@RyanLewis-Johnson-wq6xs]

Never stop learning those who stopped learning have stopped living.

[@ArunabhaDey-u5j]

😂 hilarious and thoughtful

[@gregmackinnon3663]

Love the way you make everything so clear. Thank you✨

[@srisaishravan5512]

I am gonna write jee in future and i love integrals too, thanks for uploading!

[@Mystical_Poet]

Man!! I wish a question like this comes in JEE Adv. when I write the test next year. This is lot easier compared to other JEE Adv. questions!!

[@walter274]

Most test are made with some relatively easy problems. The idea is that you don't want a test taker to look at the exam, and be so freaked out that they are so overwhelmed with anxiety that you can't get an accurate read on their ability. It doesn't work perfectly.

[@talcual2138]

Never stop doing math, those who stop doing math, stop thinking.

[@ryanwilson9555]

I tried integration by substitution seeing that I could substitute out 1-x^2 to make evaluating d^2/dx^2[(1-x^2)^5] a lot easier. I also changed the derivative notation d^2/dx^2 to d^2/d(insert new variable here)^2 to match the new variable I was differentiating with respect to. In the end, I got 2 as my answer.

[@johnpro2847]

Thanks.. sounds like a Morse code lesson which I would love to learn as well as calculus

[@stephenp6411]

Beautiful solution.

[@adamcionoob3912]

I solved it the same way as you did. Nice problem.

[@RyanLewis-Johnson-wq6xs]

You are amazing!

[@giftmathschem1989]

I am inspired since I am a tutor myself ❤

[@maths01n]

Learnt alot ❤

[@RyanLewis-Johnson-wq6xs]

Integrate[4x^3D[(1-x^2)^5,{x,2}],{x,0,1}]=2 It’s in my head.

[@lalbi-x6z]

2:25 he forgot to multiply by dx in both equations. dv is a differential and cannot be equal to a function that is by itself. the same thing applies for du.

[@grexy]

Thats just how the shorthand notation for integration by parts is, and such notation is seen all throughout calculus

[@bjornfeuerbacher5514]

@@grexy Every time I've seen integration by parts done by using du and dv, the dx was written explicitly. Leaving this out is not "shorthand", it's simply wrong. If you want to leave out the dx, you have to write u and v, not du and dv.

[@lalbi-x6z]

@@grexy whether multiplying two things or not is not a matter of notation. secondly, if you were to make an argument where you said, many people confuses the dx in this type of situation so it’s fine that he does too, you’d be wrong.

[@Maths786]

If "f" is a differentiable function on the interval [0, 1], with the following boundary conditions: f(0) = 0 f(1) = 1 Then, find the minimum value of the integral: ∫ from 0 to 1 of (f'(x))² dx. Please sir do this question also!

[@jbasanth4896]

If you take f(x) =x, the answer will be 1 and actually that will be the answer

[@alexicon2006]

​@@jbasanth4896Proving that it is the answer is gonna be the main chunk of it tho.

[@bjornfeuerbacher5514]

Sounds like a problem which can be solved with the calculus of variations - do you know that?

[@bjornfeuerbacher5514]

@@jbasanth4896 So solving by guessing the answer, and not providing any proof that the answer is actually correct? I don't think that will be enough. :D

[@Maths786]

@@jbasanth4896 why

[@holyshit922]

This d^2/dx^2 suggests integration by parts twice

[@Abby-hi4sf]

Thank you

[@Dedicate25]

Jee adv question :)

[@suyunbek1399]

when will he finally stutter and say never stop living those who stop living stop learning

[@s1ng23m4n]

Looks like an integeral from some polyomial(after some distributing and takin derivatives) shit) Eazy i guess

[@virat-k9g]

We have only 2 to 3 minutes to solve this or any question . think the hardwork of aspirants 🎉

[@grimke4036]

I think it's possible, provided that you studied sufficiently. Also Prime Newtons explains a lot between writing and his pace is rather slow, so that everyone can catch up to it. I think that 3 minutes is still a reasonable time if you know what to do.

[@Yeah_its_desi]

No this was easy, can easily be done under 3 minutes

[@h617-tf8dp]

In jee adv i think they have more time

[@virat-k9g]

@h617-tf8dp its only 3 hours of maths chemistry and physics paper for each subject carrying 20 question in frist term , then in second term they do this similarly but questions are increased and questions also

[@virat-k9g]

This is not a question there are 30 question of maths and physics and chemistry . this is easy question but once take the whole paper 😂 of advance then say 3 minutes is sufficient

[@mohammedamohamed1885]

I have solved more simply and more fast by u sabistitution u=1-x^2

[@bjornfeuerbacher5514]

And what did you do with the d²/dx² ?

[@千尺丨乇爪几]

why didn't u solve it by tublar method

[@allenjonesstyles6112]

Tabular​@@千尺丨乇爪几