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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 MPSetChAttrs('ch0001','ch0',[[5,1,-3,-1,0],[7,1,-4,-1,0],[9,2,-4,-1,0],[],[],[],[22,4,-11,-2,-1]]) MPInlineChar(0) MPNNCalcTopLeft(document.mpch0001ph,'') MPDeleteCode('ch0001')  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

[Notes]

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