Disk method

Definition

The disk method is a technique for finding the volume of a solid of revolution by slicing it into disks. It involves integrating the area of these circular slices perpendicular to the axis of rotation.

5 Must Know Facts For Your Next Test

1. The formula for the disk method is $$V = \pi \int_{a}^{b} [R(x)]^2 \, dx$$ where $R(x)$ is the radius of the disk at position $x$.
2. The method applies to solids generated by rotating a function around an axis, typically the x-axis or y-axis.
3. Disks are perpendicular to the axis of rotation, and their radii are determined by the function being rotated.
4. Integral limits $(a$ and $b)$ represent the interval over which you are rotating the function.
5. If rotating around an axis other than x or y, adjustments must be made to account for the distance from that axis.

Review Questions

• What is the integral formula used in the disk method?
• How do you determine the radius of a disk when using this method?
• In what scenarios would you use adjustments in applying the disk method?

Related terms

Solid of Revolution: A three-dimensional object obtained by rotating a two-dimensional shape around an axis.

Washer Method: A technique similar to the disk method but used when there is a hole in the middle, resulting in washers instead of disks.

\text{Volume}: \text{The amount of space occupied by a solid object, typically measured in cubic units.}