I have recently done a proof (verification) of the divergence theorem of a sphere centered at the origin with no problem using polar coordinates to complete the LHS and spherical coordinates on the RHS. I now have a problem that gives a sphere at x^2 + y^2 + z^2 + 2*x - 2*y =7. Before the rhs volume integral was very nice in spherical coordinates when the spere was at 0,0,0. I need to determine either side of the divergence theorem. del dotted with F gives me a constant but not 0. Where should I start (is the surface integral easier to deal with than the volume integarl)? The obivous choice of spherical coordinates from before does not look so great now? Could I take advantage of the y = 0 surface in the surface integral case?