Question

The value of ${\int }_0^{\pi }|cosx|dx$ is

• A. 1
• B. 2
• C. 0
• D. 4

Answer 1

The correct option is B 2

We have,
$I={\int }_o^{\pi }|cosx|dx={\int }_o^{\pi /2}|cosx|dx+{\int }_{\pi /2}^{\pi }|cosx|dx$
$\Rightarrow I={\int }_o^{\pi /2}cosxdx-{\int }_{\pi /2}^{\pi }cosxdx=[sinx{]}_0^{\pi /2}-[sinx{]}_{\pi /2}^{\pi }$
$\Rightarrow I=(1-0)-(0-1)=2$