By using the properties of definite integrals,evaluate the integral $\begin{align*}\int\limits_0^2x\sqrt{2-x}dx \end{align*}$

Question

$\begin{array}{1 1} \frac{16 \sqrt 2 } {15} \\ \frac{32 \sqrt 2}{15} \\ \frac{30 \sqrt 8}{32} \\ \frac{16 \sqrt 4}{15} \end{array} $