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The value of \({\int }_{\frac{-\pi }{2}}^{\frac{\pi }{2}}\frac{1}{1+{e}^{\sin x}}dx\) is [JEE Main 2020, 5 Sep (Shift 1)…

Q1

The value of \({\int }_{\frac{-\pi }{2}}^{\frac{\pi }{2}}\frac{1}{1+{e}^{\sin x}}dx\) is

[JEE Main 2020, 5 Sep (Shift 1)]

a

\(\frac{\pi}{4}\)

b

\(\pi\)

c

\(\frac{3 \pi}{2}\)

d

\(\frac{\pi}{2}\)

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