Chapter 8, Problem 16PS

Proof Suppose that $f(a)=f(b)=g(a)=g(b)=0$ and the second derivatives of f and g are continuous on the closed interval [a, b]. Prove that

${\displaystyle {\int }_a^{b}f(x)g^a(x)dx={\displaystyle {\int }_a^b{f}^a(x)g(x)dx}}$