Q. The value of $\int_{- \pi}^{\pi}{\left( 1 - x^{2} \right)\sin{x\cos^{2}{x\ dx}}}$ is
A) 0
B) $\pi - \frac{\pi^{2}}{3}$
C) $2\pi - \pi^{3}$
D) $\frac{7}{2} - 2\pi^{3}$
Explanation
(a)
Since, the given function is an odd function.
$\therefore\ I = \int_{- \pi}^{\pi}{\left( 1 - x^{2} \right)\sin{x\cos^{2}{x\ dx = 0}}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.