A) \[1-\frac{\pi }{4}\]
B) \[1+\frac{\pi }{4}\]
C) \[\frac{\pi }{4}\]
D) \[\frac{\pi }{2}\]
Correct Answer: C
Solution :
Using gamma function, \[\int_{0}^{\pi /2}{\,\,{{\cos }^{2}}x\,dx}\]=\[\frac{\Gamma \left( \frac{3}{2} \right)\Gamma \left( \frac{1}{2} \right)}{2\Gamma (2)}=\frac{\frac{1}{2}\Gamma \left( \frac{1}{2} \right)\Gamma \left( \frac{1}{2} \right)}{2.1.\Gamma (1)}=\frac{\pi }{4}\].
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