If f(x) = * 20 c e^ x x, & |x| , 2 2, & otherwise ., then _ , - ,… - Vidyadip

MCQ

If $f(x) = \left\{ {\begin{array}{*{20}{c}}{{e^{\cos x}}\sin x,}&{|x|\, \le 2}\\{2,}&{{\rm{otherwise}}}\end{array}} \right.$, then $\int_{\, - \,2}^{\,3} {f(x)\,dx} $ is equal to

A
$0$
B
$1$
✓
$2$
D
$3$

✓

Answer

Correct option: C.

$2$

c
(c) $\int_{ - 2}^3 {f(x)\,dx = } \int_{ - 2}^2 {f(x)\,dx + \int_2^3 {\,f(x)\,dx} } $

$\because$ ${e^{\cos x}}\sin x$ is an odd function

$\therefore \,\int_{ - 2}^3 {f(x)\,dx} $

$= \int_{ - 2}^2 {{e^{\cos x}}\sin x\,dx + \int_2^3 {2\,dx = 0 + 2\,(3 - 2) = 2} } $.

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