Q. If $P = \int_{0}^{3\pi}{f(\cos^{2}{x)\ dx\ }}$ and $Q = \int_{0}^{\pi}{f(\cos^{2}{x)\ dx}}$, then
A) $P - Q = 0$
B) $P - 2\ Q = 0$
C) $P - 3\ Q = 0$
D) $P - 5\ Q = 0$
Explanation
(c)
Given, $P = \int_{0}^{3\pi}{f(\cos^{2}{x)dx}}$ …(i)
and $Q = \int_{0}^{\pi}{f(\cos^{2}{x)\ dx}}$ …(ii)
From Eq. (i)
$P = 3\int_{0}^{\pi}{f(\cos^{2}{x)dx}}$
$\Rightarrow P = 3Q\ \Rightarrow P - 3Q = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.