Answer:
Option D
Explanation:
|x|=1
$\therefore$ $x\pm 1$
$\therefore$ $y=xe^{|x|}$=$\begin{cases}x.e^{-x},& -1<x<0\\x.e^{x}, & 0<x<1\end{cases}$
$\therefore$ Required area = $|\int_{-1}^{0} x e^{-x}dx+\int_{0}^{1} xe^{x}dx|$
= $|\left[ -x. e^{-x}-e^{-x}\right]_{-1}^{0}+\left\{ x.e^{x}-e^{x}\right\}^{1}_{0}|$
$=|\left\{(0-1)-(1.e-e)\right\}|+|\left\{(e-e)-(0-1)\right\}|$
=1+1=2 sq units
