A) \[\frac{5\pi }{512}\]
B) \[\frac{3\pi }{512}\]
C) \[\frac{\pi }{512}\]
D) None of these
Correct Answer: B
Solution :
\[I=\int_{0}^{\pi /2}{{{\sin }^{4}}x{{\cos }^{6}}x.dx}\] \[\Rightarrow I=\frac{\Gamma \,(5/2)\,\Gamma \,(7/2)}{2\Gamma (6)}\], (Applying gamma function) Þ \[I=\frac{3/2.1/2.\sqrt{\pi }.5/2.3/2.1/2.\sqrt{\pi }}{2.5.4.3.2.1}\]\[=\frac{3\pi }{512}\].You need to login to perform this action.
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