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

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Paul
August 7, 2018


Calculus III - Assignment 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  10 evaluate the given line integral.  Follow the direction of C as given in the problem statement.

 

1. Evaluate  where C is the portion of  from  and

 

2. Evaluate  where C is the line segment from  to

 

3. Evaluate  where C is the left half of the circle centered at the origin of radius 6 with counter clockwise rotation.

 

4. Evaluate  where C is given by  for  .

 

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

 

6. Evaluate  where C is given by  for  .

 

7.  Evaluate  where C is the circle centered at the origin of radius 1 centered on the x-axis at  .   See the sketches below for the direction. 

 

            

 

 

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

 

9.  Evaluate  where C is the upper half of the circle centered at the origin of radius 1 with the clockwise rotation followed by the line segment form  to  which in turn is followed by the lower half of the circle centered at the origin of radius 3 with the clockwise rotation.   See the sketch below for the direction.

 

10. Evaluate  where C is the triangle with vertices ,  and  with the clockwise rotation.

 

11. 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 portion of  from  to .

 

12. 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 .

 

13. Evaluate  for each of the following curves.

            (a) C is the line segment from  to .

(b) C is the line segment from  to .

 

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

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

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