1. The problem statement, all variables and given/known data Let f be of class C1 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 C1 that f' is continuous. Maybe change of variables?