# The value of the integral

Question:

The value of the integral $\int_{0}^{\pi}|\sin 2 x| d x$ is

Solution:

$\mathrm{I}=\int_{0}^{\pi}|\sin 2 \mathrm{x}| \mathrm{d} \mathrm{x}$

$\mathrm{I}=2 \int_{0}^{\pi / 2}|\sin 2 \mathrm{x}| \mathrm{dx}=2 \int_{0}^{\pi / 2} \sin 2 \mathrm{xd} \mathrm{x}$

$\mathrm{I}=2\left[\frac{-\cos (2 \mathrm{x})}{2}\right]_{0}^{\pi / 2}=2$