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)

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