A plane lamina with constant density $\rho ( x , y ) = 6$ occupies a region in the $x y$-plane bounded by a simple closed path $C$. Its moments of inertia about the axes are
$$I _ { x } = - \frac { \rho } { 3 } \int _ { C } y ^ { 3 } d x \text { and } I _ { y } = \frac { \rho } { 3 } \int _ { C } x ^ { 3 } d y$$
Find the moments of inertia about the axes, if $C$ is a rectangle with vertices $( 0,0 ) , ( 4,0 )$, $( 4,5 )$ and $( 0,5 )$

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The Answer of A plane lamina with constant density $\rho ( x , y ) = 6$ occupies a region in the $x y$-plane bounded by a simple closed path $C$. Its moments of inertia about the axes are
$$I _ { x } = - \frac { \rho } { 3 } \int _ { C } y ^ { 3 } d x \text { and } I _ { y } = \frac { \rho } { 3 } \int _ { C } x ^ { 3 } d y$$
Find the moments of inertia about the axes, if $C$ is a rectangle with vertices $( 0,0 ) , ( 4,0 )$, $( 4,5 )$ and $( 0,5 )$

A Plane Lamina with Constant Density ρ(x,y)=6\rho ( x , y ) = 6ρ(x,y)=6

A Plane Lamina with Constant Density $\rho ( x , y ) = 6$