Question

The value of the integral $\underset{0}{\overset{\pi }{\int }}|\sin 2x|dx$ is

Answer 1

$I=\underset{0}{\overset{\pi }{\int }}|\sin 2x|dx$
$\Rightarrow I=2\underset{0}{\overset{\pi /2}{\int }}|\sin 2x|dx$
$\Rightarrow I=2\underset{0}{\overset{\pi /2}{\int }}\sin 2xdx$
$\Rightarrow I=2{\left[\frac{-\cos \left(2x\right)}{2}\right]}_0^{\pi /2}=2$