Question

Calculate the following integrals.
${\int }_{\pi /4}^{\pi /2}\sin 2xdx.$

Answer 1

${\int }_{\pi /4}^{\pi /2}\sin 2xdx$

$=\frac{-1}{2}{\left[\cos 2x\right]}_{\pi /4}^{\pi /2}$

$=\frac{-1}{2}[-1-0]$

$=\frac{1}{2}$