Answer
$$
\int_{0}^{\pi / 2} \cos 5 x \cos 2 x d x =-\frac{5}{21}
$$
Work Step by Step
$$
\int_{0}^{\pi / 2} \cos 5 x \cos 2 x d x
$$
If we look at the section of n the Table of Integrals , we see that the closest entry is number 80 with $a=5 , b=2:$
$$
\begin{aligned}
\int_{0}^{\pi / 2} \cos 5 x \cos 2 x d x &=\left[\frac{\sin (5-2) x}{2(5-2)}+\frac{\sin (5+2) x}{2(5+2)}\right]_{0}^{\pi / 2} \quad\left[\begin{array}{l}
a=5 \\
b=2
\end{array}\right] \\
&=\left[\frac{\sin 3 x}{6}+\frac{\sin 7 x}{14}\right]_{0}^{\pi / 2}\\
&=\left(-\frac{1}{6}-\frac{1}{14}\right)-0\\
&=\frac{-7-3}{42}\\
&=-\frac{5}{21}
\end{aligned}
$$
