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 - Practice Problems
 Line Integrals Previous Chapter Stokes' Theorem Previous Section

## Divergence Theorem

1. Use the Divergence Theorem to evaluate  where  and S is the surface of the sphere of radius 4 with  and .  Note that all three surfaces of this solid are included in S. [Solution]

2. Use the Divergence Theorem to evaluate  where  and S is the surface of the box with ,  and .  Note that all six sides of the box are included in S. [Solution]

3. Use the Divergence Theorem to evaluate  where  and S is the surface of the solid bounded by  and the plane  .  Note that both of the surfaces of this solid included in S. [Solution]

Problem Pane
 Stokes' Theorem Previous Section Line Integrals Previous Chapter

[Notes]

 © 2003 - 2018 Paul Dawkins