washer method

Finding the volume of a solid of revolution with a hole through it, by slicing into ring-shaped washers.

The washer method finds the volume of a solid of revolution when the region does not touch the axis of revolution, integrating the area of an outer disk minus an inner disk: $V=\pi\int_a^b \big([f(x)]^2-[g(x)]^2\big)\,dx$ .

Examples

Revolving the region between $y=x$ and $y=x^2$ on $[0,1]$ about the $x$ -axis uses the washer method.