Use the fact that $\displaystyle 0 \le xe^{-x} \le e^{-1}$ on $\displaystyle \left[0, 2\right]$ to estimate $\displaystyle \int_{0}^{\,2} {xe^{-x}}\, dx\,.$

$\displaystyle \le \int_{0}^{\,2} {xe^{-x}}\, dx \le$