A) \[\frac{4\pi }{3}\]
B) \[\frac{2\pi }{3}\]
C) \[\pi \]
D) \[\frac{\pi }{3}\]
Correct Answer: D
Solution :
\[\int\limits_{0}^{\pi /3}{\frac{\cos x+\sin x}{\sqrt{1+\sin 2x}}}dx\] \[=\int\limits_{0}^{\pi /3}{\frac{\cos x+\sin x}{\sqrt{{{\sin }^{2}}x+{{\cos }^{2}}x+2\sin x\cos x}}}dx\] \[=\int\limits_{0}^{\pi /3}{\frac{\cos x+\sin x}{\sqrt{{{(\cos x+\sin x)}^{2}}}}}dx=\int\limits_{0}^{\pi /3}{dx}=\frac{\pi }{3}\]
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