Thread: Not 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.

Originally Posted by Nichelle14

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.

use integration by parts
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

Hello, Nichelle14!

Did you follow Malaygoel's solution?

Compute:

if and

Integrate by parts . . .

Let:

Then:


We have: .

. .

. . -1