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

Calculus III - Assignment Problems
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 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]

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