Application of Integrals — Maths STD 12 Science — Question
Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Integrals1 Mark
MCQ
The area bounded by $y=x e^{|x|}$ and $|x|=1$ is:
A
$4$
B
$6$
C
$1$
✓
$2$
✓
Answer
Correct option: D.
$2$
$=\text{I}=\int\limits^1_{-1}\text{y}\text{dx}$
$=\int\limits^1_{-1}\text{dx}^\text{x}\text{dx}$
$=\int\limits^1_{-1}\text{dx}^\text{-x}\text{dx}+\int\limits^1_0\text{xe}^\text{x}\text{dx}$
$=[-\text{xe}^\text{-x}+\int\text{e}^\text{-x}\text{ dx}]^0_{-1}+[\text{xe}^\text{x}-\int\text{e}^\text{x}\text{dx}]^1_0$
$=[-\text{xe}^\text{-x}-\text{e}^\text{-x}]^0_{-1}+[\text{xe}^\text{x}-\text{e}^\text{x}]^1_0$
$=-1-\text{(e}-\text{e})]+[\text{e}-\text{e}(-1)]=|-1|+|1|$
we take modulus because area can not be negative and this function is symmetry about $y$ axis.
we have to put modulus otherwise area will be zeroso,ans is $2$
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