This applet is designed to illustrate the shell method for solids of revolution.
There are three windows:
The first window shows the diagram in the x-y plane. There is an upper and lower function.
Draggable points let you control the limits of integration, the axis of revolution, and the position of the line that will become the sample shell.
The second window is the 3-D window that shows the results of the rotation.
The third window has controls and results. has a place for entering the upper and lower functions. It gives the area of the current shell, both generically and for the current location. It gives and evaluates the integral for volume, both generically and as a number, both up to the current shell, and for the whole volume.
Controls let you determine how much of the solid is shown and the viewing window.