1) The correct evaluation of $\int_{0}^{\pi/2} |\sin^{4}x|dx$ is A) $\frac{8\pi}{3}$ B) $\frac{2\pi}{3}$ C) $\frac{4\pi}{3}$ D) $\frac{3\pi}{8}$ Answer: Option DExplanation:$\int_{0}^{\pi/2} |\sin^{4}x|dx$ = $\int_{0}^{\pi/2} \sin^{4}xdx$ Applying gamma function, $2\int_{0}^{\pi/2} \sin^{4}xdx=2\frac{\Gamma(5/2).\Gamma(1/2)}{2.\Gamma(6/2)}=\frac{3\pi}{8}$
