If a region in a plane is revolved around a line in that plane, the resulting solid is called a solid of revolution, as shown in the following figure:
We can use the slicing method here:
\[V = \int^b_a A(x) \ dx \]
When we use the slicing method with solids of revolution, it is often called the disk method. Since the revolution forms a circular shape, we can say \(A(x) = \pi [f(x)]^2\):
\[V = \int^b_a \pi [f(x)]^2 \ dx \]