Math Is Fun Forum

maths4prasad

Member

Registered: 2013-08-15

Posts: 3

n th derivative

the problem is to prove that -∫(-1 to 1) u^(n-1)(x) u^(n+1)(x)dx = (-1)^n ∫(-1 to 1)u(x)u^(2n)(x)dx
here (n-1),(n+1),(2n) are n th derivatives and u(x) = (x²-1)^n
plz help me to prove above problem...

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: n th derivative

Hi;

You should latex these so they are readable.

This is a good online latex creator. It uses pull down menus and produces perfect latex every time.

http://latex.codecogs.com/editor.php

That is the LHS of your question. Refresh my memory, which polynomials are u(x)?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

maths4prasad

Member

Registered: 2013-08-15

Posts: 3

Re: n th derivative

thanks for replying..
that problem u interpreted is correct, and u(x)=\left(x^2-1)^n

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: n th derivative

Hi;

So the whole question looks like this:

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.