Calculus II, Lecture 2: Volume by slicing

Lecture 2: Volumes by Slicing.

In this lecture, we see how to calculate the volume of a three-dimensional object formed by "revolving" a graph around the y-axis. Our method is to cut up the solid into thin slices and add up the volume of each. Taking the limit as the thickness of a slice goes to zero yields an integral for computing the exact volume. For more complicated examples, these shells have holes in them are are thus called "washers".