Answer
$$\int_{0}^{\pi/2}cos5x\,cos2x\,dx=-\frac{5}{21}$$
Work Step by Step
Table of intergrals 80:
$\int_{0}^{\pi/2}cos(au)cos(bu)du=\left [\frac{sin(a-b)u}{2(a-b)}+\frac{sin(a+b)u}{2(a+b)} \right ]_{0}^{\pi/2}$
$$\int_{0}^{\pi/2}cos5x\,cos2x\,dx=$$
$$= \frac{sin(3\pi/2)u}{6}+\frac{sin7\pi/2}{14} -0$$
$$=-\frac{1}{6}-\frac{1}{14}=-\frac{5}{21}$$
