Loading Solution   
Paul's Online Math Notes
Calculus III (Practice Problems) / Line Integrals / Line Integrals of Vector Fields   [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 - Practice Problems
Multiple Integrals Previous Chapter   Next Chapter Surface Integrals
Line Integrals - Part II Previous Section   Next Section Fundamental Theorem for Line Integrals

 

1. Evaluate  where  and C is the line segment from  to . [Solution]

 

2. Evaluate  where  and C is the portion of  that is in the 4th quadrant with the counter clockwise rotation. [Solution]

 

3. Evaluate  where  and C is the portion of  from  to . [Solution]

 

4. Evaluate  where  and C is given by  for . [Solution]

 

5. Evaluate  where  and C is the upper half of the circle centered at the origin of radius 1 with counter clockwise rotation and the portion of  from  to .  See the sketch below.

[Solution]

 

6. Evaluate  where  and C is the line segment from  to  followed by portion of  from  to  which is in turn followed by the line segment from  to .  See the sketch below.

[Solution]

 

7. Evaluate  where  for each of the following curves.

            (a) C is the line segment from  to  followed by the line segment from

 to .

(b) C is the line segment from  to .

[Solution]

 

8. Evaluate  where  for each of the following curves.

            (a) C is the upper half of the circle centered at the origin of radius 4 with counter clockwise rotation.

(b) C is the upper half of the circle centered at the origin of radius 4 with clockwise rotation.

[Solution]

  

Problem Pane
Line Integrals - Part II Previous Section   Next Section Fundamental Theorem for Line Integrals
Multiple Integrals Previous Chapter   Next Chapter Surface Integrals

Calculus III (Practice Problems) / Line Integrals / Line Integrals of Vector Fields    [Notes] [Practice Problems] [Assignment Problems]

© 2003 - 2018 Paul Dawkins