Definite Integration Question 260
Question: $ \int_0^{\pi }{{{\sin }^{5}}( \frac{x}{2} )dx} $ equals
[Kurukshetra CEE 1996]
Options:
A) $ \frac{16}{15} $
B) $ \frac{32}{15} $
C) $ \frac{8}{15} $
D) $ \frac{5}{6} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \int_0^{\pi }{{{\sin }^{5}}\frac{2}{x}dx=2\int_0^{\pi /2}{{{\sin }^{5}}tdt=2.\frac{\Gamma \frac{6}{2}.\Gamma \frac{1}{2}}{2\Gamma \frac{7}{2}}=\frac{16}{15}}} $ .
BETA
