Find the Mass and the Moments of Inertia $I _ { x } , I _ { y }$

Short Answer

Find the mass and the moments of inertia $I _ { x } , I _ { y }$ , and $I _ { 0 }$ and the radii of gyration $\bar { x }$ and $\bar { y }$ for the lamina occupying the region $R$ , where $R$ is the region bounded by the graphs of the equations $x = 2 \sqrt { y } , x = 0$ , and $y = 2$ , and having the mass density $\rho ( x , y ) = x y$ .