Q. If $I_{1} = \int_{0}^{3\pi}{f(\cos^{2}{x)}}dx$ and $I_{2} = \int_{0}^{\pi}f(\cos{\ ^{2\ \ }x)dx,\ }then$
A) $I_{1} = I_{2}$
B) $3I_{1} = I_{2}$
C) $I_{1} = 3I_{2}$
D) $I_{1} = 5I_{2}$
Explanation
(c)
$\because\ \cos^{2}{(\pi + x) = \cos^{2}x}$
$\Rightarrow \ I_{1} = \int_{0}^{3\pi}{f(\cos^{2}{x)dx = 3\int_{0}^{\pi}{f(\cos^{2}{x)dx}}}}$
$= 3I_{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.