A) \[\frac{16}{15}\]
B) \[\frac{32}{15}\]
C) \[\frac{8}{15}\]
D) \[\frac{5}{6}\]
Correct Answer: A
Solution :
\[\int_{0}^{\pi }{{{\sin }^{5}}\frac{2}{x}dx=2\int_{0}^{\pi /2}{{{\sin }^{5}}tdt=2.\frac{\Gamma \frac{6}{2}.\Gamma \frac{1}{2}}{2\Gamma \frac{7}{2}}=\frac{16}{15}}}\].
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