Shell Method

The shell method in integral calculus produces the volume of a function rotated around an axis, as modeled by an infinite number of hollow pipes, all infinitely thin.

Mathematically, take

$2\pi \int _{a}^{b}p(x)h(x)dx$

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.

Here the function p(.) is the distance from the axis and h(.) is generally the function being rotated. The values for a and b are the limits of integration, the starting and stopping points of the rotated shape.

See also: Disc Method