The area bounded by the curve | y | + 1 2 = e^ - | x | is - Vidyadip

MCQ

The area bounded by the curve $\left| y \right| + \frac{1}{2} = {e^{ - \left| x \right|}}$ is

✓
$2(1 - ln\,2)$
B
$\frac {1}{2}(1 - ln\,2)$
C
$2(ln\,2 + 1)$
D
$\frac {1}{2}(1 + ln\,2)$

✓

Answer

Correct option: A.

$2(1 - ln\,2)$

a
$|y|+\frac{1}{2}=e^{-|x|}$

$|y|=e^{-|x|}-\frac{1}{2}$

$e^{-x}-\frac{1}{2}=0 \Rightarrow x=\ln 2$

Required area $ = 4\int\limits_0^{\ln 2} {\left( {{e^{ - x}} - \frac{1}{2}} \right)} dx$

Solving, we get the required area $=2[1-\ln 2]$

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