Question

The area (in square units) bounded by $y=x{e}^{\left|x\right|}$ and lines $\left|x\right|=1,y=0$, is

• A. $4$
• B. $6$
• C. $1$
• D. $2$

Answer 1

The correct option is D $2$

R.E.F image

Area $=2{\int }_0^{1}x{e}^{x}dx$

$=2[x{e}^x-{\int }_0^1{e}^{x}dx{]}_0^1$

$=2[x{e}^x-e^x{]}_0^1$

$=2[e-e+(-1\left)\right]$

$=2\left[1\right]$

$=2$

D is correct