The value of $\int_{-\pi / 2}^{\pi / 2} \frac{1}{1+\mathrm{e}^{\sin \mathrm{x}}} \mathrm{dx}$ is:

JEE Main · 2020 · 05 Sep 2020 · Shift 1 · Definite Integrals

The value of

\int_{- π /2}^{π /2} \frac{1}{1 + e ^{s i n x}} dx

is:

Answer: (B)

Call the integral

I

. Replacing

x

- x

over the symmetric limits turns the integrand into

\frac{1}{1 + e ^{- s i n x}} = \frac{e ^{s i n x}}{1 + e ^{s i n x}}

. Adding this form to the original, the two integrands sum to

1

, so

2 I = \int_{- π /2}^{π /2} d x = π

, and

I = \frac{π}{2}

JEE Main · 2020 · 05 Sep 2020 · Shift 1 · Single correct option

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