Q. $\int_{}^{}\sqrt{1 + \cos x}dx$ 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) $\sqrt{2}\sin{\frac{x}{2} + c}$
Explanation
(b)
$\int_{}^{}\sqrt{1 + \cos x}\ dx$
$= \int_{}^{}\sqrt{2\cos^{2}\frac{x}{2}}\ dx$
$= \sqrt{2}\int_{}^{}{\cos\frac{x}{2}}\ dx = 2\sqrt{2}.\sin{\frac{x}{2} + c}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.