Let : R [0, ) be the density of a rectangular object R C R with...

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Let : R [0, ) be the density of a rectangular object R C R with positive mass. Assume is continuous on R aside from a set of zero Jordan measure. (3a) For a system of point masses at positions x1,...,xN R" with masses m,. about the origin 0 R" is given by N mi||xi||. i=1 ..., my, the moment of inertia (*) You may take this physical principle for granted. Let P be a partition of R with subrectangles {R}iel Use Riemann sums to exhibit a discrete approximation of the moment of inertia for the object R. When applying (*), briefly explain what you treat as a point mass and why this assumption is reasonable. (3b) Using (3a), derive the integral formula for the moment of inertia I = [ R ||x||26(x)dV. Let : R [0, ) be the density of a rectangular object R C R with positive mass. Assume is continuous on R aside from a set of zero Jordan measure. (3a) For a system of point masses at positions x1,...,xN R" with masses m,. about the origin 0 R" is given by N mi||xi||. i=1 ..., my, the moment of inertia (*) You may take this physical principle for granted. Let P be a partition of R with subrectangles {R}iel Use Riemann sums to exhibit a discrete approximation of the moment of inertia for the object R. When applying (*), briefly explain what you treat as a point mass and why this assumption is reasonable. (3b) Using (3a), derive the integral formula for the moment of inertia I = [ R ||x||26(x)dV.