Cracking The Ap Calculus ab Exam 2018

    =   πx

Each disk is infinitesimally thin, so its thickness is dx; if you add up the volumes of all the disks, you’ll
get the entire volume. The way to add these up is by using the integral, with the endpoints of the interval
as the limits of integration. Therefore, to find the volume, evaluate the integral.

Now let’s generalize this. If you have a region whose area is bounded by the curve y = f(x) and the x-axis
on the interval [a, b], each disk has a radius of f(x), and the area of each disk will be

π[f(x)]^2

To find the volume, evaluate the integral.

π [f(x)]^2 dx

This is the formula for finding the volume using disks.

Example 1: Find the volume of the solid that results when the region between the curve y = x and the x-
axis, from x = 0 to x = 1, is revolved about the x-axis.

As always, sketch the region to get a better look at the problem.