Question

The correct evaluation of $\int_{0}^{\pi}{\left| \sin^{4}x \right|dx}$ is

• A. $\frac{8\pi}{3}$
• B. $\frac{2\pi}{3}$
• C. $\frac{4\pi}{3}$
• D. $\frac{3\pi}{8}$

Answer 1

Answer: (D)

$\frac{3\pi}{8}$

Answer 2

$\int_{0}^{\pi}{\ \left| \ \sin^{4}x\ \right|\ dx = 2\int_{0}^{\pi/2}{\sin^{4}xdx}}$

Applying gamma function,

$2\int_{0}^{\pi/2}{\sin^{4}xdx} = 2\frac{\Gamma(5/2).\Gamma(1/2)}{2.\Gamma(6/2)} = \frac{3\pi}{8}$.