A) \[\frac{1}{2},\frac{\pi }{4}\]
B) \[1,\frac{\pi }{2}\]
C) \[1,1\]
D) None of these
Correct Answer: A
Solution :
\[I=\int{\sqrt{2}\,\sqrt{1+\sin x}\,\,dx=\sqrt{2}\int{\left( \sin \frac{x}{2}+\cos \frac{x}{2} \right)\,dx}}\]\[=2\int{\sin \left( \frac{\pi }{4}+\frac{x}{2} \right)}\,\,dx=-4\cos \,\,\left( \frac{x}{2}+\frac{\pi }{4} \right)+c\] On comparing, \[a=\frac{1}{2},\,b=\frac{\pi }{4}.\]You need to login to perform this action.
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