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Paul
August 7, 2018

Calculus III - Assignment Problems
 Multiple Integrals Previous Chapter Next Chapter Surface Integrals 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

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