Paul's Online Math Notes
Calculus III (Assignment Problems) / Line Integrals / Fundamental Theorem for Line Integrals   [Notes] [Practice Problems] [Assignment Problems]

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
Multiple Integrals Previous Chapter   Next Chapter Surface Integrals
Line Integrals of Vector Fields Previous Section   Next Section Conservative Vector Fields

 Fundamental Theorem for Line Integrals

 

1. Evaluate  where  and C is given by  with .

 

2. Evaluate  where  and C is given by  with .

 

3. Evaluate  where  and C is right half of the ellipse given by  with clockwise rotation.

 

4. Compute  where  and C is the circle centered at the origin of radius 5 with the counter clockwise rotation.  Is  independent of path?  If it is not possible to determine if  is independent of path clearly explain why not.

 

5. Compute  where  and C is the circle centered at the origin of radius 5 with the counter clockwise rotation.  Is  independent of path?  If it is not possible to determine if  is independent of path clearly explain why not.

 

6. Evaluate  where  and C is the line segment from  to  followed by the line segment from  to .

 

7. Evaluate  where  and C is the upper half of  with clockwise rotation followed by the right half of  with counter clockwise rotation.  See the sketch below.

 

Line Integrals of Vector Fields Previous Section   Next Section Conservative Vector Fields
Multiple Integrals Previous Chapter   Next Chapter Surface Integrals

Calculus III (Assignment Problems) / Line Integrals / Fundamental Theorem for Line Integrals    [Notes] [Practice Problems] [Assignment Problems]

© 2003 - 2018 Paul Dawkins