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