Evaluate $\int\!\!\int _{\mathcal{D}}\sqrt{x^2+y^2}\,dA$, where $\mathcal{D}$ is the domain in Figure 4

$\begin{array}{ll} F: x^2+y^2=16\quad G: (x-2)^2+y^2=4\\R_f=4 \quad R_g=2 \end{array}$

$\int\!\!\int _{\mathcal{D}}\sqrt{x^2+y^2}\,dA=$