A) \[\frac{\pi }{4}\]
B) \[\frac{\pi }{2}\]
C) zero
D) 1
Correct Answer: A
Solution :
\[I=\int_{0}^{\pi /2}{\frac{\sqrt{\sin x}dx}{\sqrt{\cos x}+\sqrt{\sin x}}}\] ...(i) \[I=\int_{0}^{\pi /2}{\frac{\sqrt{\sin (\pi /2-x)}}{\sqrt{\cos (\pi /2-x)}+\sqrt{\sin (\pi /2-x)}}}dx\] \[I=\int_{0}^{\pi /2}{\frac{\sqrt{\cos x}}{\sqrt{\sin x}+\sqrt{\cos x}}}dx\] ?.(ii) on adding equation (i) and (ii) \[2I=\int_{0}^{\pi /2}{dx}\] \[\Rightarrow \] \[I=\frac{\pi }{4}\]
You need to login to perform this action.
You will be redirected in
3 sec
