Question

Calculate the following integrals.
${\int }_0^{\pi /4}8\sin 3xdx.$

Answer 1

${\int }_0^{\pi /4}8\sin 3xdx$

$=\frac{-8}{3}{\left[\cos 3x\right]}_0^{\pi /4}$

$=\frac{-8}{3}[\frac{-1}{\sqrt{2}}-1]$

$=\frac{8}{3}[1+\frac{1}{\sqrt{2}}]$