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

Calculus III - Assignment Problems
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Line Integrals - Part II Previous Section   Next Section Fundamental Theorem for Line Integrals

 Line Integrals of Vector Fields

 

1. Evaluate  where  and C is the portion of  that is in the 1st, 4th and 3rd quadrant with the clockwise orientation.

 

2. Evaluate  where  and C is the line segment from  to .

 

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

 

4. Evaluate  where  and C is given by  for .

 

5. Evaluate  where  and C is the line segment from  to .

 

6. Evaluate  where  and C is the portion of the spiral on the y-axis given by  for .

 

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

 

8. Evaluate  where  and C is the portion of  in the 2nd quadrant with clockwise rotation followed by the line segment from  to .  See the sketch below.

 

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

 

10. Evaluate  where  for each of the following curves.

            (a) C is the top half of the circle centered at the origin of radius 1 with the counter clockwise rotation.

(b) C is the bottom half of  with clockwise rotation.

 

11. Evaluate  where  for each of the following curves.

            (a) C is the portion of  from  to .

(b) C is the line segment from  to .

 

14. Evaluate  where  for each of the following curves.

            (a) C is the line segment from  to .

(b) C is the line segment from  to .

 

13. Evaluate  where  for each of the following curves.

            (a) C is the portion of  in the 1st quadrant with counter clockwise rotation.

(b) C is the portion of  in the 1st quadrant with clockwise rotation.

 

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

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

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