Question

${\int }_0^{\pi }\sqrt{\frac{1+\cos 2x}{2}}dx$ equals to.

• A. $0$
• B. $2$
• C. $4$
• D. $-2$

Answer 1

Answer: (A)

$0$

Let $I={\int }_0^{\pi }\sqrt{\frac{(\cos 2x+1)}{2}}dx$
$\cos 2x=2{\cos }^{2}x-1$

$⟹\frac{1+\cos 2x}{2}={\cos }^{2}x$

$⟹I={\int }_0^{\pi }\cos dx=|\sin x{|}_0^{\pi }=\sin \pi -\sin 0=0$