An example was worked-out in detail, showing how the choice of which type of triple integration region to use can greatly influence how easy the problem is to solve. The example also showed how cylindrical coordinates can help evaluate an integral. In this case, the cylindrical coordinates were aligned along the y-axis instead of the usual z-axis.
This led to a presentation of how, in general, to evaluate triple integrals in cylindrical coordinates and spherical coordinates (section 13.8 of the textbook).