Q. If $I_{1} = \int_{0}^{\pi/4}{\sin^{2}x}\ dx$ and $I_{2} = \int_{0}^{\frac{\pi}{4}}{\cos^{2}x}\ dx$, then
A) $I_{1} = I_{2}$
B) $I_{1} < I_{2}$
C) $I_{1} > I_{2}$
D) $I_{2} = I_{1} + \frac{\pi}{4}$
Explanation
(b)
For $x\epsilon\left( 0,\frac{\pi}{4} \right)\cos^{2}x > \sin^{2}x$
$\Rightarrow \int_{0}^{\frac{\pi}{4}}{\cos^{2}x}\ dx > \int_{0}^{\frac{\pi}{4}}{\sin^{2}x}\ dx$
$\Rightarrow I_{1} < I_{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.