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]. This shape is z-simple. 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. In these cases, it is easier to investigate [math]rz[/math]-plane and set up the integral there. That is why, we can move [math]\theta[/math] to either end of integral since a full rotation is done independently from the other variables.