Q. The value of $\int_{0}^{\pi/2}{\frac{1 + 2\cos x}{(2 + {{cos\ }{x)}}^{2}}\ dx\ }$is
A) $- \frac{1}{2}$
B) 2
C) $\frac{1}{2}$
D) None of these
Explanation
(c)
$\int_{0}^{\pi/2}{\frac{1 + 2\cos x}{(2 + {\cos{x)}}^{2}}dx}$
$= \int_{0}^{\pi/2}{\frac{d}{dx}\ \left( \frac{\sin x}{2 + \cos x} \right)dx}$
$= \left\lbrack \frac{\sin x}{2 + \cos x} \right\rbrack_{0}^{\pi/2} = \frac{1}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.