Question

Answer any three of the following
Evaluate ${\int }_0^{\pi }|\cos x|dx$

Answer 1

We have,

${\int }_0^{\pi }|\cos x|dx$

$={\int }_0^{\pi /2}\cos xdx$$+{\int }_{\pi /2}^{\pi }-\cos xdx$

$=[\sin x{]}_0^{\pi /2}$$+[-\sin x{]}_{\pi /2}^{\pi }$

$=(1-0)+(1-0)$

$=2$

Hence, this is the answer.