The animation explains the [math]\theta rz[/math] space for [math]\int_{r_1}^{r_2}\int_{h_{1^{\left(z\right)}}}^{h_2\left(z\right)}\int_0^{2\pi}rf\left(r,\theta,z\right)d\theta drdz[/math]. When the shape is [math]r[/math]-simple or the shape is already split into [math]r[/math]-simple regions, each [math]z[/math]-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.