Question

$\int \sqrt{1+\cos x}dx$ is equal to

• A. $2\sqrt{2}\cos \frac{x}{2}+C$
• B. $2\sqrt{2}\sin \frac{x}{2}+C$
• C. $\sqrt{2}\cos \frac{x}{2}+C$
• D. $\sqrt{2}\sin \frac{x}{2}+C$

Answer 1

Answer: (B)

$\int \sqrt{1+\cos x}dx=\sqrt{2}\int \cos \left(\frac{x}{2}\right)dx$
$=2\sqrt{2}\sin \left(\frac{x}{2}\right)+c$
$\left[\because 1+\cos x=2{\cos }^2\frac{x}{2}\right]$