Discussion Forum

The area bounded by $y=xe^{|x|}$ and lines |x|=1 , y=0 is 

Answer:

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