Question

The value of the integral ${\int }_0^{\pi }\sqrt{\frac{1+\cos 2x}{2}}dx$ is

• A. -2
• B. 2
• C. 0
• D. -3

Answer 1

The correct option is B 2

${\int }_0^{\pi }\sqrt{\frac{1+cos2x}{2}}dx={\int }_0^{\pi }\left|cosx\right|dx$
${\int }_0^{\pi /2}cosxdx-{\int }_{\pi /2}^{\pi }cosxdx$
$sinx{\int }_0^{\pi /2}-sinx{\int }_{\pi /2}^{\pi }$
$=1-(-1)$
$=2$
Hence, option 'B' is correct.