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Exam 15: Section 3: Vector Analysis

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Find the value of the line integral Find the value of the line integral , where and . (Hint: If F is conservative, the integration may be easier on an alternate path.) , where Find the value of the line integral , where and . (Hint: If F is conservative, the integration may be easier on an alternate path.) and Find the value of the line integral , where and . (Hint: If F is conservative, the integration may be easier on an alternate path.) . (Hint: If F is conservative, the integration may be easier on an alternate path.)

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Question 1
Correct Answer:
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A

Find the value of the line integral Find the value of the line integral . (Hint: If is conservative, the integration may be easier on an alternate path.) . (Hint: If Find the value of the line integral . (Hint: If is conservative, the integration may be easier on an alternate path.) is conservative, the integration may be easier on an alternate path.) Find the value of the line integral . (Hint: If is conservative, the integration may be easier on an alternate path.)

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(Multiple Choice)
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Question 2
Correct Answer:
Verified

B

To allow a means of escape for workers in a hazardous job 70 meters above ground level, a slide wire is installed. It runs from their position to a point on the ground 70 meters from the base of the installation where they are located. Find the work done by the gravitational force field for a 185-pound man moving the length of the slide wire for the path To allow a means of escape for workers in a hazardous job 70 meters above ground level, a slide wire is installed. It runs from their position to a point on the ground 70 meters from the base of the installation where they are located. Find the work done by the gravitational force field for a 185-pound man moving the length of the slide wire for the path . Round your answer to the nearest integer. . Round your answer to the nearest integer.

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Question 3
Correct Answer:
Verified

D

Find the value of the line integral Find the value of the line integral where and . (Hint: If F is conservative, the integration may be easier on an alternate path.) where Find the value of the line integral where and . (Hint: If F is conservative, the integration may be easier on an alternate path.) and Find the value of the line integral where and . (Hint: If F is conservative, the integration may be easier on an alternate path.) Find the value of the line integral where and . (Hint: If F is conservative, the integration may be easier on an alternate path.) . (Hint: If F is conservative, the integration may be easier on an alternate path.)

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Question 4

Calculate the line integral along Calculate the line integral along for and C is any path starting at the point and ending at . for Calculate the line integral along for and C is any path starting at the point and ending at . and C is any path starting at the point Calculate the line integral along for and C is any path starting at the point and ending at . and ending at Calculate the line integral along for and C is any path starting at the point and ending at . .

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Question 5

Find the value of the line integral Find the value of the line integral . (Hint: If is conservative, the integration may be easier on an alternate path.) . (Hint: If Find the value of the line integral . (Hint: If is conservative, the integration may be easier on an alternate path.) is conservative, the integration may be easier on an alternate path.) Find the value of the line integral . (Hint: If is conservative, the integration may be easier on an alternate path.)

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Question 6

A stone weighing 2 pounds is attached to the end of a four-foot string and is whirled horizontally with one end held fixed. It makes 1 revolution per second. Find the work done by the force F that keeps the stone moving in a circular path. [Hint: Use Force = (mass)(centripetal acceleration).] Round your answer to two decimal places, if required.

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Question 7

Evaluate the line integral Evaluate the line integral using the Fundamental Theorem of Line Integrals, where C is the smooth curve from to . using the Fundamental Theorem of Line Integrals, where C is the smooth curve from Evaluate the line integral using the Fundamental Theorem of Line Integrals, where C is the smooth curve from to . to Evaluate the line integral using the Fundamental Theorem of Line Integrals, where C is the smooth curve from to . .

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Question 8

Determine whether or not the vector field is conservative. Determine whether or not the vector field is conservative.

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Question 9

Find the value of the line integral Find the value of the line integral , where and . (Hint: If F is conservative, the integration may be easier on an alternate path.) , where Find the value of the line integral , where and . (Hint: If F is conservative, the integration may be easier on an alternate path.) and Find the value of the line integral , where and . (Hint: If F is conservative, the integration may be easier on an alternate path.) Find the value of the line integral , where and . (Hint: If F is conservative, the integration may be easier on an alternate path.) . (Hint: If F is conservative, the integration may be easier on an alternate path.)

(Multiple Choice)
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Question 10

Find the value of the line integral Find the value of the line integral on the closed path consisting of line segments from to from to and then from to where . (Hint: If F is conservative, the integration may be easier on an alternate path.) on the closed path consisting of line segments from Find the value of the line integral on the closed path consisting of line segments from to from to and then from to where . (Hint: If F is conservative, the integration may be easier on an alternate path.) to Find the value of the line integral on the closed path consisting of line segments from to from to and then from to where . (Hint: If F is conservative, the integration may be easier on an alternate path.) from Find the value of the line integral on the closed path consisting of line segments from to from to and then from to where . (Hint: If F is conservative, the integration may be easier on an alternate path.) to Find the value of the line integral on the closed path consisting of line segments from to from to and then from to where . (Hint: If F is conservative, the integration may be easier on an alternate path.) and then from Find the value of the line integral on the closed path consisting of line segments from to from to and then from to where . (Hint: If F is conservative, the integration may be easier on an alternate path.) to Find the value of the line integral on the closed path consisting of line segments from to from to and then from to where . (Hint: If F is conservative, the integration may be easier on an alternate path.) where Find the value of the line integral on the closed path consisting of line segments from to from to and then from to where . (Hint: If F is conservative, the integration may be easier on an alternate path.) . (Hint: If F is conservative, the integration may be easier on an alternate path.)

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Question 11

Calculate the line integral along Calculate the line integral along for and C is any path starting at the point and ending at . for Calculate the line integral along for and C is any path starting at the point and ending at . and C is any path starting at the point Calculate the line integral along for and C is any path starting at the point and ending at . and ending at Calculate the line integral along for and C is any path starting at the point and ending at . .

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Question 12

Find the work done by the force field Find the work done by the force field in moving an object from P to Q. in moving an object from P to Q. Find the work done by the force field in moving an object from P to Q.

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Question 13

Evaluate the line integral using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. Evaluate the line integral using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. C: circle clockwise from to C: circle Evaluate the line integral using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. C: circle clockwise from to clockwise from Evaluate the line integral using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. C: circle clockwise from to to Evaluate the line integral using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. C: circle clockwise from to

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Question 14

Evaluate the line integral using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. Evaluate the line integral using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. C: a smooth curve from to C: a smooth curve from Evaluate the line integral using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. C: a smooth curve from to to Evaluate the line integral using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. C: a smooth curve from to

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Question 15

Find the value of the line integral Find the value of the line integral where C is an ellipse from to . (Hint: If is conservative, the integration may be easier on an alternate path.) where C is an ellipse Find the value of the line integral where C is an ellipse from to . (Hint: If is conservative, the integration may be easier on an alternate path.) from Find the value of the line integral where C is an ellipse from to . (Hint: If is conservative, the integration may be easier on an alternate path.) to Find the value of the line integral where C is an ellipse from to . (Hint: If is conservative, the integration may be easier on an alternate path.) . (Hint: If Find the value of the line integral where C is an ellipse from to . (Hint: If is conservative, the integration may be easier on an alternate path.) is conservative, the integration may be easier on an alternate path.)

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Question 16

Evaluate the line integral Evaluate the line integral using the Fundamental Theorem of Line Integrals, where C is the line segment from to . using the Fundamental Theorem of Line Integrals, where C is the line segment from Evaluate the line integral using the Fundamental Theorem of Line Integrals, where C is the line segment from to . to Evaluate the line integral using the Fundamental Theorem of Line Integrals, where C is the line segment from to . .

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Question 17

Find the value of the line integral Find the value of the line integral where and . (Hint: If F is conservative, the integration may be easier on an alternate path.) where Find the value of the line integral where and . (Hint: If F is conservative, the integration may be easier on an alternate path.) and Find the value of the line integral where and . (Hint: If F is conservative, the integration may be easier on an alternate path.) Find the value of the line integral where and . (Hint: If F is conservative, the integration may be easier on an alternate path.) . (Hint: If F is conservative, the integration may be easier on an alternate path.)

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Question 18
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