Compute integral of x*f'(x)*f(x) dx from a to b if

the integral of f^2(x)dx from a to b equals 2 and f(a)=f(b)=0. :confused:

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- Jun 1st 2006, 05:28 PMNichelle14Not too sure what to do
Compute integral of x*f'(x)*f(x) dx from a to b if

the integral of f^2(x)dx from a to b equals 2 and f(a)=f(b)=0. :confused: - Jun 1st 2006, 08:20 PMmalaygoelQuote:

Originally Posted by**Nichelle14**

integral of {x}*{f'(x)*f(x)} dx from a to b

={x*f^2(x)/2 from a to b} - {integral of 1*f^2(x)/2 dx from a to b}

={b*f^2(b)- a*f^2(a)} -2/2

=b*0 -a*0 -1

= -1 - Jun 1st 2006, 08:54 PMSoroban
Hello, Nichelle14!

Did you follow Malaygoel's solution?

Quote:

Compute:

if and

Let:

Then:

We have: .

. .

. .**-1**