The **disc method ** (also called *disc integration*) is a way to find the volume of solids of revolution. You can use it for two dimensional rotated objects where the axis of rotation is also the boundary (edge) *and* cross sections (thin slices) are perpendicular to the axis of rotation. If the axis of rotation isn’t a boundary, use the washer method instead.

The formula for the disc method is:

## Disc Method: Example

**Example question:** Find the volume of the shape created when the equation x = 2 is revolved around the x-axis.

**Solution:**

Step 1: **Draw the graph and rotate it** around. If you have trouble visualizing this (which is very common!), try this great tool at Desmos.com. I used it to rotate the graph and create the following image of the object of revolution (shown in light blue):

Step 2: **Put the function into the integral formula.** That’s the function that created the main “skin” of the shape: the boundary that you rotated. For this example, that’s y = e^{-x}:

Step 3: Fill in the x-boundaries. The left boundary (a) for this example is 0; The right boundary (b) is ln(5):

Step 4: **Calculate the integral** using the usual methods or a calculator. For this particular integral you’ll need a combination of u substitution and the power function rule for integrals. I used Symbolab’s calculator to get the solution:

**12π/25**

*That’s it!*

If you have difficulty visualizing rotations, the following video shows an example of how to visualize rotating a graph around the x-axis.