Q. $\int_{0}^{\pi}{\cos^{3}{x\ dx\ }is}$ equal to
A) 0
B) 1
C) $- 1$
D) $\frac{1}{2\sqrt{2}}$
Explanation
(a)
Let $I = \int_{0}^{\pi}{\cos^{3}{x\ dx}}$ …(i)
$\Rightarrow I = \int_{0}^{\pi}{\cos^{3}{(\pi - x)dx = - \int_{0}^{\pi}{\cos^{3}{x\ dx}}}}$ …(ii)
On adding Eqs. (i) and(ii), we get
$2I = 0 \Rightarrow I = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.