Definite-Integration Question 505
Question: $ \int_0^{\pi /2}{{{\sin }^{2}}x{{\cos }^{3}}x},dx= $
[RPET 1984, 2003]
Options:
A) 0
B) $ \frac{2}{15} $
C) $ \frac{4}{15} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Using gamma function, $ \int_0^{\pi /2}{{{\sin }^{2}}x{{\cos }^{3}}xdx=\frac{\Gamma ,( \frac{3}{2} ),\Gamma 2}{2\Gamma ( \frac{7}{2} )}=\frac{2}{15}} $ .
BETA
