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A Plane Lamina with Constant Density ρ(x,y)=12\rho ( x , y ) = 12

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A plane lamina with constant density ρ(x,y) =12\rho ( x , y ) = 12 occupies a region in the xy-plane bounded by a simple closed path C. Its moments of inertia about the axes are Ix=ρ3Cy3dx and Iy=ρ3Cx3dyI _ { 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) ( 0,5 ) .

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External Supply

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