Question

Find the value of $\underset{-\frac{\pi }{2}}{\overset{\frac{\pi }{2}}{\int }}|\sin x|dx$.

Answer 1

We have $|\sin x|$ is an even function as $|\sin (-x)|=|\sin x|$.

Now,

$\underset{-\frac{\pi }{2}}{\overset{\frac{\pi }{2}}{\int }}|\sin x|dx$

$=$$2\underset{0}{\overset{\frac{\pi }{2}}{\int }}\sin xdx$ [ Using property of definite integral]

$=2[-\cos x{]}_{x=0}^{x=\frac{\pi }{2}}$

$2$.