Definite Integration Question 225
Question: $ \int_0^{\pi /2}{{{\cos }^{2}}xdx=} $
Options:
A) $ 1-\frac{\pi }{4} $
B) $ 1+\frac{\pi }{4} $
C) $ \frac{\pi }{4} $
D) $ \frac{\pi }{2} $
Show Answer
Answer:
Correct Answer: C
Solution:
Using gamma function, $ \int_0^{\pi /2}{{{\cos }^{2}}xdx} $ = $ \frac{\Gamma ( \frac{3}{2} )\Gamma ( \frac{1}{2} )}{2\Gamma (2)}=\frac{\frac{1}{2}\Gamma ( \frac{1}{2} )\Gamma ( \frac{1}{2} )}{2.1.\Gamma (1)}=\frac{\pi }{4} $ .
BETA
