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 $\rho ( x , y ) = x y$.

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The Answer of 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 $\rho ( x , y ) = x y$.

Find the Mass and the Moments of Inertia Ix,IyI _ { x } , I _ { y }Ix​,Iy​

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