Volumes by Integration

Volumes by Integration: Disk Method Procedure

Most students find that it helps to follow the procedure below when working this type of problem.

   1. Make a sketch. Show the area involved, sketch in the disk and label the thickness dx or dy.

   2. Write the equation for the volume of the disk, dV. The volume of a disk is area time thickness (dx or dy).

                            dV=pr²dx    or    dV=pr²dy

   3. Put the equation in terms of x (if dx) or y (if dy). Then choose limits. (Use the sketch to visualize the disk sweeping over the volume.)

   4. Integrate and solve.

Practice Problems