We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
© 2016 Shmoop University, Inc. All rights reserved.
GO TO SAT PREP GO TO ACT PREP

Disks and Washers Exercises

Example 1

Let R be the region bounded by y = ln x and the x-axis on the interval [1,2]. Find an integral expression for the volume of the solid obtained by rotating R around

(a) the x-axis

(b) the line x = 2

Example 2

Let R be the region bounded by y = x3, the y-axis, and the line y = 8. Find an integral expression for the volume of the solid obtained by rotating R around

(a) the y-axis

(b) the line y = 8

Example 3

Let R be the region bounded by the graphs y = 1 – x, y = x2 + 1, and the line x = 1.

Find an integral expression for the volume of the solid obtained by rotating R around the line

(a) y = 0

(b) y = 2

(c) y = -2

(d) y = 5

Example 4

Let R be the portion of the unit circle that falls in the first quadrant. Find an integral expression for the volume of the solid obtained by rotating R around the line

(a) y = 0

(b) y = 2

(c) x = 1

(d) x = -1

Advertisement