Our math professor gave us this take-home project: Consider a solid in the shape of the region D inside the surface x^2 / (z^3 - 1)^2 + y^2 / (z^3 + 1)^2 = 1 If the density of the solid at the point (x,y,z) is x^2 + y^2 + z^2 then determine the mass of this solid. A GOOD CHANGE OF VARIABLES WILL HELP. I understand how to do the problem but I can't get a change of variables that works well. I've tried cylindrical and spherical and many other random ones. Can anyone suggest a good change of variables to use? My teacher said that the cross sections for integration are in the shape of ellipses. Thank you!