The value of \[\int_{\,0}^{\,\pi /2}{\frac{{{2}^{\sin x}}}{{{2}^{\sin x}}+{{2}^{\cos x}}}dx}\] is [Karnataka CET 1999; Kerala (Engg.) 2005]

The value of \[\int_{\,0}^{\,\pi /2}{\frac{{{2}^{\sin x}}}{{{2}^{\sin

1.	The value of \[\int_{\,0}^{\,\pi /2}{\frac{{{2}^{\sin x}}}{{{2}^{\sin x}}+{{2}^{\cos x}}}dx}\] is [Karnataka CET 1999; Kerala (Engg.) 2005]
A.	\[\frac{\pi }{4}\]
B.	\[\frac{\pi }{2}\]
C.	\[\pi \]
D.	\[2\pi \]
Answer» B. \[\frac{\pi }{2}\]

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The value of \[\int_{\,0}^{\,\pi /2}{\frac{{{2}^{\sin x}}}{{{2}^{\sin x}}+{{2}^{\cos x}}}dx}\] is [Karnataka CET 1999; Kerala (Engg.) 2005]

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