The value of _ - / 2 ^ / 2 1 1+ e ^ x d x - Vidyadip

MCQ

The value of $\int \limits_{-\pi / 2}^{\pi / 2} \frac{1}{1+ e ^{\sin x}} d x$

A
$\pi$
B
$\frac{3 \pi}{2}$
C
$\frac{\pi}{4}$
✓
$\frac{\pi}{2}$

✓

Answer

Correct option: D.

$\frac{\pi}{2}$

d
$I=\int_{-\pi / 2}^{\pi / 2} \frac{1}{1+e^{\sin x}} d x$

Apply King property

$I=\int_{E \pi / 2}^{\pi / 2} \frac{1}{1+e^{-\sin x}} d x=\int_{-\pi / 2}^{\pi / 2} \frac{e^{\sin x}}{1+e^{\sin x}} d x$

$\begin{array}{l}2 I =\int_{-\pi / 2}^{\pi / 2} d x =\pi \\I =\frac{\pi}{2}\end{array}$

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