Answer
$0 \leq \int_{0}^{2} x~e^{-x}~dx \leq \frac{2}{e}$
Work Step by Step
On the interval $0 \leq x \leq 2$:
$0 \leq x~e^{-x} \leq \frac{1}{e}$
Therefore, by Property 8:
$0(2-0) \leq \int_{0}^{2} x~e^{-x}~dx \leq \frac{1}{e}(2-0)$
$0 \leq \int_{0}^{2} x~e^{-x}~dx \leq \frac{2}{e}$
