Question

Evaluate the following integral:

${\int }_{-\pi /4}^{\pi /4}|\sin x|dx$

Answer 1

Consider,

$I={\int }_{-\pi /4}^{\pi /4}|\sin x|dx$

$I={\int }_{-\pi /4}^0-\sin xdx+{\int }_0^{\pi /4}\sin xdx$

$I={\cos x|}_{-\pi /4}^0-{(-\cos x)|}_0^{\pi /4}$

$I=1-\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}+1=2$