_ - , /2 ^ , /2 , x 1 + ^2 x e^ - ^2 x dx is equal to - Vidyadip

MCQ

$\int_{ - \,\pi /2}^{\,\pi /2} {\,\frac{{\sin x}}{{1 + {{\cos }^2}x}}{e^{ - {{\cos }^2}x}}dx} $ is equal to

A
$2{e^{ - 1}}$
B
$1$
✓
$0$
D
None of these

✓

Answer

Correct option: C.

$0$

c
(c) $I = \int_{ - \pi /2}^{\pi /2} {\frac{{\sin x}}{{1 + {{\cos }^2}x}}{e^{ - {{\cos }^2}x}}dx} $

$\because \frac{\sin x}{1+{{\cos }^{2}}x}{{e}^{-{{\cos }^{2}}x}}$ is an odd function,

$\therefore$ $I = 0$.

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