Question

Evaluate ${\int }_{\frac{-\pi }{4}}^{\frac{\pi }{4}}\sin xdx$

Answer 1

We know that,

$=\underset{-\frac{\pi }{4}}{\overset{\frac{\pi }{4}}{\int }}\sin xdx$

$=-{\left[\cos x\right]}_{\frac{-\pi }{4}}^{\frac{\pi }{4}}$

$=-[\cos \frac{\pi }{4}-\cos \left(\frac{-\pi }{4}\right)]$

$=-[\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}]$

$=0$

Hence, this is the required solution