Definite Integration Question 262
Question: $ \int_0^{\pi /2}{{{\sin }^{4}}x{{\cos }^{6}}xdx} $ equals
[RPET 1999]
Options:
A) $ \frac{5\pi }{512} $
B) $ \frac{3\pi }{512} $
C) $ \frac{\pi }{512} $
D) None of these
Show Answer
Answer:
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)
therefore $ 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} $ .
BETA
