A) 0
B) \[\frac{2}{15}\]
C) \[\frac{4}{15}\]
D) None of these
Correct Answer: B
Solution :
Using gamma function, \[\int_{0}^{\pi /2}{{{\sin }^{2}}x{{\cos }^{3}}xdx=\frac{\Gamma \,\left( \frac{3}{2} \right)\,\Gamma 2}{2\Gamma \left( \frac{7}{2} \right)}=\frac{2}{15}}\].
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