Q. $\int_{0}^{\frac{\pi}{2}}\frac{\cos x}{1 + \sin x}\ dx$ is equal to
A) $\log 2$
B) $2\log 2$
C) $({\log{2)}}^{2}$
D) $\frac{1}{2}\log 2$
Explanation
(a)
Let $I = \int_{0}^{\frac{\pi}{2}}\frac{\cos x}{1 + \sin x}\ dx$
$= \left\lbrack \log\left( 1 + \sin x \right) \right\rbrack_{0}^{\frac{\pi}{2}}$
$= \log 2 - \log 1 = \log 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.