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

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]

  

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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]

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