The value of the integral $\int\limits_0^\pi {|{{\sin }\,}2x|dx}$ is ___________.
Answer (integer)
2
Solution
$\begin{aligned} & \text { Let } I=\int_0^\pi|\sin 2 x| d x
\\\\ & =2 \int_0^{\pi / 2}|\sin 2 x| d x \quad[\because \sin 2 x \text { is periodic function }]
\\\\ & =2 \int_0^{\pi / 2} \sin 2 x \,d x[\sin 2 x \text { is positive in range }(0, \pi / 2)]
\\\\ & =2\left[\frac{-\cos 2 x}{2}\right]_0^{\pi / 2} \\\\ & =-[\cos \pi-\cos 0]=-(-1-1)=2 \end{aligned}$
About this question
Subject: Mathematics · Chapter: Definite Integration · Topic: Properties of Definite Integrals
This question is part of PrepWiser's free JEE Main question bank. 216 more solved questions on Definite Integration are available — start with the harder ones if your accuracy is >70%.