Question

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

Answer 1

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

Let $\sin x=t⟹dt=\cos xdxx\to 0\to \pi /2t\to 0\to 12{\int }_0^{1}tdt2{\frac{t^2}{2}|}_0^1=1$