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Calculus III (Practice Problems) / Multiple Integrals / Double Integrals in Polar Coordinates   [Notes] [Practice Problems] [Assignment Problems]

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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
Applications of Partial Derivatives Previous Chapter   Next Chapter Line Integrals
Double Integrals over General Regions Previous Section   Next Section Triple Integrals

 

1. Evaluate  where D is the region in the 3rd quadrant between  and . [Solution]

 

2. Evaluate   where D is the bottom half of . [Solution]

 

3. Evaluate  where D is the portion of  in the 1st quadrant. [Solution]

 

4. Use a double integral to determine the area of the region that is inside  and outside . [Solution] 

 

5. Evaluate the following integral by first converting to an integral in polar coordinates.

 

 

[Solution]

 

6. Use a double integral to determine the volume of the solid that is inside the cylinder , below  and above the xy-plane. [Solution]

 

7. Use a double integral to determine the volume of the solid that is bounded by  and . [Solution] 

 

Problem Pane
Double Integrals over General Regions Previous Section   Next Section Triple Integrals
Applications of Partial Derivatives Previous Chapter   Next Chapter Line Integrals

Calculus III (Practice Problems) / Multiple Integrals / Double Integrals in Polar Coordinates    [Notes] [Practice Problems] [Assignment Problems]

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