Paul's Online Math Notes
[Notes]
Notice

On August 21 I am planning to perform a major update to the site. I can't give a specific time in which the update will happen other than probably sometime between 6:30 a.m. and 8:00 a.m. (Central Time, USA). There is a very small chance that a prior commitment will interfere with this and if so the update will be rescheduled for a later date.

I have spent the better part of the last year or so rebuilding the site from the ground up and the result should (hopefully) lead to quicker load times for the pages and for a better experience on mobile platforms. For the most part the update should be seamless for you with a couple of potential exceptions. I have tried to set things up so that there should be next to no down time on the site. However, if you are the site right as the update happens there is a small possibility that you will get a "server not found" type of error for a few seconds before the new site starts being served. In addition, the first couple of pages will take some time to load as the site comes online. Page load time should decrease significantly once things get up and running however.

Paul
August 7, 2018

Calculus III - Assignment Problems
 Applications of Partial Derivatives Previous Chapter Next Chapter Line Integrals Triple Integrals Previous Section Next Section Triple Integrals in Spherical Coordinates

## Triple Integrals in Cylindrical Coordinates

1. Evaluate  where E is the region bounded by  and  in the 1st octant.

2. Evaluate  where E is the region above , below  and inside the cylinder .

3. Evaluate  where E is the region between  and  inside the cylinder .

4. Evaluate  where E is the region bounded by  and  with .

5. Evaluate  where E is the region between the two planes  and   inside the cylinder .

6. Evaluate  where E is the region bounded by  and  with .

7. Use a triple integral to determine the volume of the region bounded by , and  in the 1st octant.

8. Use a triple integral to determine the volume of the region bounded by , and  in the 1st octant.

9. Use a triple integral to determine the volume of the region below , above  and inside the cylinder .

10. Evaluate the following integral by first converting to an integral in cylindrical coordinates.

11. Evaluate the following integral by first converting to an integral in cylindrical coordinates.

12. Use a triple integral in cylindrical coordinates to derive the volume of a cylinder of height h and radius a.

 Triple Integrals Previous Section Next Section Triple Integrals in Spherical Coordinates Applications of Partial Derivatives Previous Chapter Next Chapter Line Integrals

[Notes]

 © 2003 - 2018 Paul Dawkins