A) \[\frac{8\pi }{3}\]
B) \[\frac{2\pi }{3}\]
C) \[\frac{4\pi }{3}\]
D) \[\frac{3\pi }{8}\]
Correct Answer: D
Solution :
\[\int_{0}^{\pi }{\text{ }\left| \text{ }{{\sin }^{4}}x\text{ } \right|\text{ }dx=2\int_{0}^{\pi /2}{{{\sin }^{4}}x\,dx}}\] Applying gamma function, \[2\int_{0}^{\pi /2}{{{\sin }^{4}}x\,dx}=2\frac{\Gamma (5/2).\Gamma (1/2)}{2.\Gamma (6/2)}=\frac{3\pi }{8}\].
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