Question

$\stackrel{1}{\underset{0}{\int }}x{e}^{x}dx=$

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is A $1$

$I=\stackrel{1}{\underset{0}{\int }}x{e}^{x}dx..............\left(1\right)$
$\int x{e}^x=x{e}^x-\int 1.e^{x}dx$
$=x{e}^x-e^x$
$=e^x(x-1)$
From (1)
$I=\stackrel{1}{\underset{0}{\int }}x{e}^x{d}^x-\left[e^x\right(x-1){]}_0^1$
$=e(1-1)-e^0(0-1)$
$=e\times 0-1(-1)$
$=0+1$
$I=1$