AP Calculus AB and BC glossary

Disk method

The disk method computes the volume of a solid of revolution by slicing it into circular disks perpendicular to the axis of rotation and integrating the area of each. It applies when the region being rotated touches the axis, leaving no hole.

V = \pi \int_a^b \left(R(x)\right)^2 dx

Each slice is a circle of radius equal to the distance from the axis to the curve, so its area is $\pi R^2$ . Integrating those areas along the axis accumulates the volume.

The mistake

Squaring only part of the radius. When rotating about a line such as $y = 2$ , the radius is $2 - f(x)$ and the entire expression must be squared.

Appears in: Unit 8: Applications of Integration