Question

The value of ${\int }_0^{\pi }\left|\cos x\right|dx$ is

• A. $2\pi$
• B. $2$
• C. $2/\pi$
• D. $\pi$

Answer 1

The correct option is B $2$

${\int }_0^{\pi }\left|\cos x\right|dx$
$={\int }_0^{\pi /2}\cos xdx-{\int }_{\pi /2}^0\cos xdx$
$={\left[\sin x\right]}_0^{\pi /2}-{\left[\sin x\right]}_{\pi /2}$
$=\sin \frac{\pi }{2}-\sin 0-\sin \pi +\sin \frac{\pi }{2}$
$=1+1$
$2$