Question

Evaluate ${\int }_0^{\pi /2}\sin x/2\cos x/2dx$

Answer 1

${\int }_0^{\pi /2}\sin x/2\cos x/2dx{\int }_0^{\pi /2}\frac{1}{2}\left(2\sin x/2\cos x/2\right)dx\frac{1}{2}{\int }_0^{\pi /2}\sin xdx\frac{1}{2}{(-\cos x)|}_0^{\pi /2}=\frac{1}{2}$