Compute integral $\int_0^a{f'(x)\cdot f(x)}dx$ what is the integral of the following function:
$\int_0^a{f'(x)\cdot f(x)}dx$
Not quite sure how to integrate it.

Alternative hint: if you integrate by parts, you obtain
$$\int_0^a f'(x)f(x)\,dx = -\int_0^af(x)f'(x)\,dx + \left[f(x)f(x) \right]_0^a $$
