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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

## Line Integrals of Vector Fields

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

[Notes]

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