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