Q. $\int_{0}^{2\pi}{\left( \sin x + \left| \sin x \right| \right)dx\ is\ equal\ to}$
A) 4
B) 0
C) 1
D) 8
Explanation
(a)
We have , $\int_{0}^{2\pi}{(\sin{x + |\sin{x|\ )dx}}}$
$= \int_{0}^{\pi}{(\sin{x + \sin{x)dx + \int_{\pi}^{2\pi}{(\sin{x - \sin{x)\ \ dx}}}}}}$
$= \int_{0}^{\pi}{2\sin{x\ dx + 0 = 2\lbrack - \cos{x\left. \ \ \right\rbrack_{0}^{\pi}}}}$
$= - 2(\cos{\pi - \cos{0) = 4}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.