Definite-Integration Question 507
Question: The correct evaluation of $ \int_0^{\pi }{| ,{{\sin }^{4}}x, |,dx} $ is
[MP PET 1993]
Options:
A) $ \frac{8\pi }{3} $
B) $ \frac{2\pi }{3} $
C) $ \frac{4\pi }{3} $
D) $ \frac{3\pi }{8} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ \int_0^{\pi }{| {{\sin }^{4}}x |dx=2\int_0^{\pi /2}{{{\sin }^{4}}x,dx}} $ Applying gamma function, $ 2\int_0^{\pi /2}{{{\sin }^{4}}x,dx}=2\frac{\Gamma (5/2).\Gamma (1/2)}{2.\Gamma (6/2)}=\frac{3\pi }{8} $ .
BETA
