A) 0
B) 1
C) 2
D) 3
Correct Answer: C
Solution :
Let \[I=\int_{0}^{\pi /2}{\frac{{{(\sin x+\cos x)}^{2}}}{\sqrt{{{\sin }^{2}}x+{{\cos }^{2}}x+2\sin x\cos x}}}dx\] \[I=\int_{0}^{\pi /2}{\frac{{{(\sin x+\cos x)}^{2}}}{\sqrt{{{(\sin x+\cos x)}^{2}}}}}dx\] \[I=\int_{0}^{\pi /2}{(\sin x+\cos x)}dx\] \[I=[-\cos x+\sin x]_{0}^{\pi /2}\] \[I=-\cos \frac{\pi }{2}+\sin \frac{\pi }{2}+\cos 0-\sin 0\] \[I=-0+1+1-0=2\]
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