Question

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

Answer 1

We know that,

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

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

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

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

$=0$

Hence, this is the required solution