Deck 15: Section 4: Vector Analysis

Question 1

Find the maximum value of where C is any closed curve in the xy-plane, oriented counterclockwise.

A)
B)
C)
D)
E)

Answer 1

Question 2

Use Green's Theorem to calculate the work done by the force on a particle that is moving counterclockwise around the closed path C where C is the boundary of the region lying between the graphs of . Round your answer to two decimal places.

A)
B)
C)
D)
E)

Answer 2

Question 3

Set up and evaluate a line integral to find the area of the region R bounded by the graph of .

A) where
B) where
C) where
D) where
E) where

Answer 3

where

Question 4

Use a computer algebra system and the result "The centroid of the region having area A bounded by the simple closed path C is " to find the centroid of the region bounded by the graphs of and .

A)
B)
C)
D)
E)

Question 5

Use Green's Theorem to calculate the work done by the force on a particle that is moving counterclockwise around the closed path C.

A)
B)
C)
D)
E)

Question 6

Use Green's Theorem to evaluate the line integral where C is .

A)
B)
C)
D)
E)

Question 7

Use Green's Theorem to evaluate the integral where C is the boundary of the region lying inside the rectangle bounded by and outside the square bounded by .

A)
B)
C)
D)
E)

Question 8

Use Green's Theorem to evaluate the line integral where C is the boundary of the region lying between the graphs of the circle and the ellipse .

A)
B)
C)
D)
E)

Question 9

Use Green's Theorem to evaluate the integral for the path C defined as .

A)
B)
C)
D)
E)

Question 10

Use Green's Theorem to evaluate the integral for the path C: boundary of the region lying between the graphs of y = x and y = .

A)
B)
C)
D)
E)

Question 11

Use Green's Theorem to evaluate the integral for the path C: boundary of the region lying between the graphs of and .

A)
B)
C)
D)
E)

Question 12

Use a computer algebra system and the result "The area of a plane region bounded by the simple closed path C given in polar coordinates is " to find the area of the region bounded by the graphs of the polar equation .

A)
B)
C)
D)
E)

Question 13

Evaluate , where is the unit circle given by .

A)
B)
C)
D)
E)

Question 14

Use a computer algebra system and the result "The area of a plane region bounded by the simple closed path C given in polar coordinates is " to find the area of the region bounded by the graphs of the polar equation . Round your answer to two decimal places.

A)
B)
C)
D)
E)

Question 15

Verify Green's Theorem by evaluating both integrals for the path C defined as the boundary of the region lying between the graphs of and .

A)
B)
C)
D)
E)

Question 16

Verify Green's Theorem by setting up and evaluating both integrals for the path C: square with vertices (0,0), (10,0), (10,10), (0,10).

A)
B)
C)
D)
E)

Question 17

Use Green's Theorem to evaluate the integral for the path C: .

A)
B)
C)
D)
E)

Question 18

Use Green's Theorem to evaluate the integral for C: boundary of the region lying between the graphs of and .

A)
B)
C)
D)
E)