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 rectangular region with vertices $( 0,0 ) \text {, }$ $( 5,0 )$ $( 5,4 )$ and $( 0,4 )$ , and having uniform density $\rho ( x , y ) = 9$

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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 rectangular region with vertices $( 0,0 ) \text {, }$ $( 5,0 )$ $( 5,4 )$ and $( 0,4 )$ , and having uniform density $\rho ( x , y ) = 9$

Find the Mass and the Moments of Inertia IxI _ { x }Ix​

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