(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let f be of class C^{1}on [a, b], with f(a) = f(b) = 0. Show that [tex]\int_a^b xf(x)f'(x)dx[/tex] = [tex]-1/2 \int_a^b [f(x)]^2 dx[/tex].

2. Relevant equations

If F is an antiderivative of f, then [tex]\int_a^b f(t)dt = F(b) - F(a)[/tex]

3. The attempt at a solution

I'm just really not sure how to begin this one. I know that because f is of class C^{1}that f' is continuous. Maybe change of variables?

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# Homework Help: Real Analysis: Integration

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