Q. The value of $\int_{0}^{\frac{\pi}{2}}{\sin^{8}x}\ dx$ is
A) $\frac{105\pi}{32(4!)}$
B) $\frac{105\pi}{14(4!)}$
C) $\frac{105}{16\pi(4!)}$
D) None of these
Explanation
(a)
Let $I = \int_{0}^{\frac{\pi}{2}}{\sin^{8}x}\ dx = \frac{7.5.3.1}{8.6.4.2}.\frac{\pi}{2}$ [by Walli’s formula]
$= \frac{105\pi}{32(4.3.2.1)}$
$= \frac{105\pi}{32.4!}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.