Question

Evaluate :

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

• A. $0$
• B. $1$
• C. $2$
• D. None of these

Answer 1

The correct option is B $1$

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

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

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

$I=(e-0)-(e-e^0)=1$