Explanation
To evaluate \(\int_{0}^{\pi / 2}(\cos \theta-\sin 2 \theta) d \theta\) by integrating, we have
\(=\left[\sin \theta+\frac{1}{2} \cos 2 \theta\right]_{0}^{7 / 2}\)
\(\Rightarrow\) Now, we subtract the lower limit from the upper limit
\begin{array}{l}
{\left[\sin \frac{\pi}{2}+\frac{1}{2} \cos 2\left(\frac{\pi}{2}\right)\right]-\left[\sin 0+\frac{1}{2} \cos 2(0)\right]} \\
\text { with } \pi=180^{\circ}, \frac{\pi}{2}=90 \\
=\left[\sin 90+\frac{1}{2} \cos 180\right]-\left[0+\frac{1}{2} \cos 0\right] \\
=\left[1-\frac{1}{2}\right]-\left[\frac{1}{2}\right]=\frac{1}{2}-\frac{1}{2}=0
\end{array}