I don't even know what's going on. xDThank you! He'll cry for a bit but he can tough it out. My cousin spoils him anyway so he'll probably get a toy or some sweets for powering through it.
Fun fact: if anyone's interested, it's not really necessary to do a Jacobian when converting a Cartesian problem to polar/cylindrical/spherical coordinates, you just need to change the limits of integration and function to match the new variables whether it's r/theta/z or rho/phi/theta. I just did it to see if I could.
So many words