Q. $\int_{- 1}^{1}{\sin^{3}{x\cos^{2}x}}\ dx$ is equal to
A) $- 1$
B) 1
C) 0
D) None of these
Explanation
(c)
Let $I = \int_{- 1}^{1}{\sin^{3}x}\cos^{2}xdx$
Again, let $f(x) = \sin^{3}x\cos^{2}x$
$f( - x) = \sin^{3}{( - x)}\cos^{2}{( - x)}$
$= - \sin^{3}x\cos^{2}x$
$\therefore f(x)$ is an odd function.
Hence, $\int_{- 1}^{1}{\sin^{3}x}\cos^{2}xdx = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.