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, \[a=\frac{1}{2},\,b=\frac{\pi }{4}.\]
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