A) 0
B) \[\frac{\pi }{2}\]
C) \[\frac{\pi }{4}\]
D) None of these
Correct Answer: C
Solution :
Let \[I=\int_{0}^{\pi /2}{\,\,\frac{\sqrt{\cos x}}{\sqrt{\sin x}+\sqrt{\cos x}}dx}\] .....(i) and \[I=\int_{0}^{\pi /2}{\frac{\sqrt{\cos \left( \frac{\pi }{2}-x \right)}}{\sqrt{\sin \left( \frac{\pi }{2}-x \right)}+\sqrt{\cos \left( \frac{\pi }{2}-x \right)}}dx}\] \[I=\int_{0}^{\pi /2}{\frac{\sqrt{\sin x}}{\sqrt{\cos x+}\sqrt{\sin x}}}\,dx\] ?..(ii) Adding (i) and (ii), we get \[2I=\int_{0}^{\pi /2}{(1)dx=\frac{\pi }{2}\Rightarrow I=\frac{\pi }{4}}\].
You need to login to perform this action.
You will be redirected in
3 sec
