Q. The value of $\int_{- \pi}^{\pi}{\sin^{3}{x\cos^{2}{x\ dx}}}$ is equal to
A) 1
B) 2
C) 3
D) 0
Explanation
(d)
Let $f(x) = \sin^{3}{x\cos^{2}x}$
$f( - x) = - \sin^{3}{x\cos^{2}{x = - f(x)}}$
$\Rightarrow f(x)is\ an\ odd\ function$
$\therefore\int_{- \pi}^{\pi}{\sin^{3}{x\cos^{2}{x\ dx = 0}}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.