Consider a lamina occupying the region R and having the density function rho: R is the rectangular region with vertices (0, 0), (0, 3), (8, 3). rho(x, y) = ((xy)^(1/2)).
a) Find the moments of inertia Ix, Iy, and I0 about the x-axis, y-axis, and origin, respectively.
b) Find the radii of gyration with respect to the x-axis, y-axis, and origin, respectively.