Shell Method

The shell method in calculus produces the volume of a function rotated around either the x or y axis, or possibly an arbitrary horizontal or verticle line, as modeled by an infinite number of hollow pipes, all infinitely thin.

This sounds terribly confusing, but is fairly simple mathematically.

$2\pi \int _{a}^{b}p(x)h(x)dx$ if the rotation is around the x axis or

$2\pi \int _{a}^{b}p(y)h(y)dy$ if the rotation is around the y axis

p() is the distance from the axis (generally "x" or "y") and h() is generally the function being rotated. a and b are the limits of integration, the starting and stopping points of the rotated shape. (A and B are generally given in the problem.)

See also: Disc Method