Find the mass and the moments of inertia $I _ { x }$ $I _ { y } ,$ and $I _ { 0 }$ and the radii of gyration $\bar {\bar { x} }$ and $\bar {\bar { y } }$ 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 $\bar {\bar { x} }$ and $\bar {\bar { y } }$ 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 IxI _ { x }Ix​

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