Explanation

(d)
Since, $|x| = 1$
$\therefore\ x = \pm 1$
$y = xe^{| - x|} = \left\{ \begin{array}{r}
xe^{- x},\ - 1 < x < 0 \\
xe^{x},\ 0 \leq x < 1
\end{array} \right.\$
$\therefore$ Required area $= \left| \int_{- 1}^{0}{xe^{- x}dx} \right| + \left| \int_{0}^{1}{xe^{x}dx} \right|$
$= \left| \left\{ - xe^{- x} - e^{- x} \right\}_{- 1}^{0} \right| + \left| \left\{ xe^{x} - e^{x} \right\}_{0}^{1} \right|$
$= 2\ sq\ unit$