Answer
$$\int_{0}^{\pi/2}cos^{2}\theta\,d\theta=\frac{\pi}{4}$$
Work Step by Step
$$\int_{0}^{\pi/2}cos^{2}\theta\,d\theta=\int_{0}^{\pi/2}\frac{1+cos2\theta}{2}d\theta$$
$$=\left [\frac{\theta}{2}+\frac{sin2\theta}{4} \right ]_{0}^{\pi/2}$$
$$=\frac{1}{2}(\frac{\pi}{2}+0)$$
$$=\frac{\pi}{4}$$
