Question

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

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (A)

$1$

${\int }_0^{1}x{e}^{x}dx$

Integrating by parts,

Let $u=x\Rightarrow du=dx$

$dv=e^{x}dx\Rightarrow v=e^x$

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

$={[e^1-0]}_0^1-{\left[e^x\right]}_0^1$

$=e-[e-e^0]=e-e+1=1$