## Calculus: Early Transcendentals 8th Edition

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