Q. $I_{1} = \int_{0}^{\pi/2}{\sin{x\ dx,\ I_{2} = \int_{0}^{\pi/2}{\sin^{3}{x\ dx}}}}$ then
A) $I_{1} > I_{2}$
B) $I_{1} < I_{2}$
C) $I_{1} = I_{2}$
D) $I_{2} = 0$
Explanation
(a)
$\sin{x > \sin^{3}x}$
$\Rightarrow \ \int_{0}^{\pi/2}{\sin{x\ dx > \int_{0}^{\pi/2}{\sin^{3}{x\ dx}}}}$
$\Rightarrow \ I_{1} > I_{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.