A) \[\sqrt{2}\]
B) \[\sqrt{2}\,\,(\sqrt{2}-1)\]
C) 2
D) none of these
Correct Answer: A
Solution :
[A] \[I=\int\limits_{\pi /4}^{\pi /2}{\sqrt{2+\sqrt{2+\cos 4x}}\,\,dx=\int\limits_{\pi /4}^{\pi /2}{\sqrt{2-2\,\,\cos 2x\,\,dx}}}\]\[=2\int\limits_{\pi /4}^{\pi /2}{\sin xdx}\] \[=2(-\cos x)_{\pi /4}^{\pi /2}=\sqrt{2}\]
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