(Integration) Using The Slicing Method To Find The Volume Of A Solid Of Revolution

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:

Image from openstax.org (Calculus Volume 1)

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 \(A(x) = \pi [f(x)]^2\):

\[V = \int^b_a \pi [f(x)]^2 \ dx \]

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