Deck 15: Section 3: Vector Analysis

Question 1

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

A) -2
B) -1
C) 2
D) 1
E) 0

Answer 1

0

Question 2

Determine whether or not the vector field is conservative.

A) conservative
B) not conservative

Answer 2

conservative

Question 3

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

A) 3,072
B) 192
C) 6,144
D) 6,912

Answer 3

3,072

Question 4

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

A)
B)
C)
D)
E)

Question 5

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

A)
B)
C)
D)
E)

Question 6

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.)

A)
B)
C) 8
D)
E)

Question 7

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

A) 274
B) 298
C) 300
D) 30
E) 272

Question 8

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

A) 64
B) 16
C) 0
D) 256
E) 32

Question 9

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

A)
B)
C)
D)
E)

Question 10

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

A) 4
B) 8
C) -8
D) -4

Question 11

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

A) -24
B) 48
C) -48
D) 24
E) 0

Question 12

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

A)
B)
C)
D)
E)

Question 13

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

A) 243
B) 192
C) 108
D) 0
E) 12

Question 14

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.

A) 4,900
B) 25,900
C) 255
D) 12,950
E) 34,225

Question 15

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

A) 27,992
B) 55,985
C) 83,978
D) 41,989
E) 69,982

Question 16

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

A) 30
B) 15
C) 13
D) 56
E) 169

Question 17

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.

A) 201.06
B) 0.00
C) 804.25
D) 256.00
E) 12.57

Question 18

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.)

A) 99
B) 12
C) 36
D) 30
E) 0