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8. Application and integration — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths8. Application and integration1 Mark
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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