Shell integration

Shell integration (the "shell method") is a means of calculating the volume of a solid of revolution. This makes use of the so-called "representative cylinder". The idea is that a "representative rectangle" (used in the most basic forms of integration -- such as ∫ x dx) can be rotated about the axis of revolution; thus generating a hollow cylinder. Integration, as an accumulative process, can then calculate the integrated area of a "family" of cylinders.