Question

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

Answer 1

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

Let $\sin x=t⟹dt=\cos xdxx\to 0\to \pi /2t\to 0\to 1$

$⟹{\int }_0^{\pi /2}tdt{\frac{t^2}{2}|}_0^1=\frac{1}{2}$