The animation explains the [math]\theta rz[/math] space for [math]\int_{r_1}^{r_2}\int_{h_{1\left(r\right)}}^{h_2\left(r\right)}\int_0^{2\pi}rf\left(r,\theta,z\right)d\theta dzdr[/math]. Here when the shape is z-simple, for each r- infinitesimal ribbon in [math]rz[/math] plane forms an infinitesimal rectangular solid in [math]\theta rz[/math] space that transforms to a shell in [math]xyz[/math] space. So in these cases, it is easier to investigate [math]rz[/math] plane and set up the integral there; we can move [math]\theta[/math] to either end since a full rotation is done independently from the other variables.