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Calculus III (Practice Problems) / Line Integrals / Line Integrals - Part I   [Notes] [Practice Problems] [Assignment Problems]

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Paul
August 7, 2018


Calculus III - Practice Problems
Multiple Integrals Previous Chapter   Next Chapter Surface Integrals
Vector Fields Previous Section   Next Section Line Integrals - Part II

 Line Integrals
 Part I

 

For problems 1  7 evaluate the given line integral.  Follow the direction of C as given in the problem statement.

 

1. Evaluate  where C is the line segment from  to [Solution]

 

2. Evaluate  where C is the lower half of the circle centered at the origin of radius 3 with clockwise rotation.  [Solution]

 

3. Evaluate  where C is the portion of  from  to .  The direction of C is in the direction of increasing x. [Solution]

 

4. Evaluate  where C is the line segment from  to . [Solution]

 

5. Evaluate  where C is the circle centered at the origin of radius 2 centered on the y-axis at .   See the sketches below for orientation.  Note the “odd” axis orientation on the 2D circle is intentionally that way to match the 3D axis the direction.

 

            

[Solution]

 

6.  Evaluate  where C is the portion of  from  to  followed by the line segment form  to  which in turn is followed by the line segment from  to .   See the sketch below for the direction.

[Solution]

 

7.  Evaluate  where C is the upper portion of the circle centered at the origin of radius 3 from  to  in the counter clockwise rotation followed by the line segment form  to  which in turn is followed by the line segment from  to .   See the sketch below for the direction.

[Solution]

 

8. Evaluate  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]

 

9. Evaluate  for each of the following curves.

            (a) C is the portion of the circle centered at the origin of radius 2 in the 1st quadrant rotating in the clockwise direction.

(b) C is the line segment from  to .

 [Solution]

 

10. Evaluate  for each of the following curves.

            (a) C is the portion  from  to .

(b) C is the portion  from  to .

[Solution]

 

Problem Pane
Vector Fields Previous Section   Next Section Line Integrals - Part II
Multiple Integrals Previous Chapter   Next Chapter Surface Integrals

Calculus III (Practice Problems) / Line Integrals / Line Integrals - Part I    [Notes] [Practice Problems] [Assignment Problems]

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