Question

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

• A. 4 sq units
• B. 6 sq units
• C. 1 sq units
• D. 2 sq units

Answer 1

The correct option is D 2 sq units

$|x|=1$

$\therefore x=\pm 1$

$\therefore y=x{e}^{|x|}=\left\{\begin{array}{cc}x.e^{-x},& -1<x<0\\ x.e^x,& 0<x<1\end{array}\right\}$

$\therefore$ Required area $=|{\int }_{-1}^{0}x{e}^{-x}dx+{\int }_0^{1}x{e}^{x}dx|$

$=|{[-x.e^{-x}-e^{-x}]}_{-1}^0+{\{x.e^x-e^x\}}_0^1|$

$=\left|\left\{\right(0-1)-(1.e-e\left)\right\}\right|+\left|\left\{\right(e-e)-(0-1\left)\right\}\right|$

$=1+1=2$ sq units