Question

$\underset{0}{\overset{\pi }{\int }}\sqrt{1+\cos x}dx$ is equal to

• A. 2
• B. 1
• C. $2\sqrt{2}$
• D. $\sqrt{2}$

Answer 1

The correct option is C $2\sqrt{2}$

Given

${\int }_0^{\pi }\sqrt{1+\cos x}dx$

${\int }_0^{\pi }\sqrt{2{\cos }^2\frac{x}{2}}dx$

${\int }_0^{\pi }\sqrt{2}\cos \frac{x}{2}dx$

$\sqrt{2}{\int }_0^{\pi }\cos \frac{x}{2}dx$

$\sqrt{2}{\left(2\sin \frac{x}{2}\right)}_0^{\pi }$

$⟹2\sqrt{2}$