The value of \[\int_{\,0}^{\,\pi /2}{\frac{{{e}^{{{x}^{2}}}}}{{{e}^{{{x}^{2}}}}+{{e}^{{{\left( \frac{\pi }{2}\,\,-\,\,x \right)}^{2}}}}}dx}\] is [AMU 1999]

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

1.	The value of \[\int_{\,0}^{\,\pi /2}{\frac{{{e}^{{{x}^{2}}}}}{{{e}^{{{x}^{2}}}}+{{e}^{{{\left( \frac{\pi }{2}\,\,-\,\,x \right)}^{2}}}}}dx}\] is [AMU 1999]
A.	\[\pi /4\]
B.	\[\pi /2\]
C.	\[{{e}^{{{\pi }^{2}}/16}}\]
D.	\[{{e}^{{{\pi }^{2}}/4}}\]
Answer» B. \[\pi /2\]

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The value of \[\int_{\,0}^{\,\pi /2}{\frac{{{e}^{{{x}^{2}}}}}{{{e}^{{{x}^{2}}}}+{{e}^{{{\left( \frac{\pi }{2}\,\,-\,\,x \right)}^{2}}}}}dx}\] is [AMU 1999]

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