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

$\underset{0}{\overset{\pi }{\int }}\left|\sin 2x\right|dx=\frac{1}{2}\underset{0}{\overset{2\pi }{\int }}\left|\sin t\right|dt=\frac{1}{\cancel{2}}\times \cancel{2}\underset{0}{\overset{\pi }{\int }}\sin tdt=2$

               $( put x=\frac{t}{2 })$                ( since  $$\begin{gathered} {\int }_0^{2a}f\left(x\right)dx =2 {\int }_0^{a}f\left(x\right)dx if f (2a-x)= f\left(x\right) \\ here \left|\sin (2\mathrm{\pi }-\mathrm{x})\right|=\left|\sin x\right| \end{gathered}$$   )