Question

The area bounded by $y=x{e}^{\left|x\right|}$, $x-$ axis and $\left|x\right|=1$ is (in sq. units)

Answer 1

The curves are given by
$y=\{\begin{array}{cc}x{e}^{-x},& x<0\\ x{e}^x,& x\ge 0\end{array},x=\{\begin{array}{cc}-1,& x<0\\ 1,& x\ge 0\end{array}$


Required area
$=2\underset{0}{\overset{1}{\int }}x{e}^{x}dx=2\{{(x\cdot e^x)}_0^1-{\left(e^x\right)}_0^1\}$
$=2$ sq. units