Deck 16: Multiple Integration

Question 1

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A) 33
B) 1
C) 87
D) 195

Answer 1

195

Question 2

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A) - 72
B) - 18
C) - 102
D) - 12

Answer 2

- 102

Question 3

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A) - 1800
B) - 600
C) - 960
D) 720

Answer 3

720

Question 4

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A) 4
B) 120
C) 60
D) 8

Question 5

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A) - 3
B) 2
C) 13
D) 3

Question 6

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A) -
B) - 45
C) -
D) - 405

Question 7

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A) 27
B) 756
C) 108
D) 189

Question 8

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A) 300
B) 1800
C) 3000
D) 18000

Question 9

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A) -
B)
C)
D) -

Question 10

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A) 8 $\pi$
B) 4 $\pi$
C) 9 $\pi$
D) 5 $\pi$

Question 11

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A)
B)
C) 24
D) 15

Question 12

Evaluate the double integral over the given region.

- R = {(x, y): 9 $\le$ x $\le$ 10, 9 $\le$ y $\le$ 10}

A)
B)
C)
D) ln

Question 13

Evaluate the double integral over the given region.

- R = {(x, y): 9 $\le$ x $\le$ 10, 1 $\le$ y $\le$ 5}

A) 114
B) 152
C) 228
D) 76

Question 14

Evaluate the double integral over the given region.

- R =

A)
B)
C)
D) $\pi$

Question 15

Evaluate the double integral over the given region.

- R = {(x, y): 0 $\le$ x $\le$ 1, 0 $\le$ y $\le$ 1}

A)
B)
C)
D)

Question 16

Evaluate the double integral over the given region.

- R = {(x, y): 0 $\le$ x $\le$ 1, 0 $\le$ y $\le$ 1}

A)
B)
C)
D)

Question 17

Evaluate the double integral over the given region.

- R = {(x, y): 0 $\le$ x $\le$$\pi$ , 0 $\le$ y $\le$ 1}

A) 4 $\pi$
B) $\pi$
C)
D) 4 $\pi$ - 4

Question 18

Evaluate the double integral over the given region.

- R = {(x, y): 0 $\le$ x $\le$ 6, 0 $\le$ y $\le$ 4}

A) ln 7
B) ln 7 ln 5
C) 5 ln 7
D) ln 35

Question 19

Evaluate the double integral over the given region.

- R = {(x, y): 0 $\le$ x $\le$ 1, 0 $\le$ y $\le$ 2}

A)
B)
C) -
D)

Question 20

Find the average value of the function f over the given region.

-f(x, y) = 2x + 8y; R = {(x, y): 0 $\le$ x $\le$ 1, 0 $\le$ y $\le$ 1}

A) 10
B) 5
C) 6
D) 9

Question 21

Find the average value of the function f over the given region.

-f(x, y) = 10x + 3y; R = {(x, y): 0 $\le$ x $\le$ 2, 0 $\le$ y $\le$ 10}

A) 15
B) 25
C)
D) 10

Question 22

Find the average value of the function f over the given region.

-f(x, y) = 5x + 10y over the triangle with vertices , , and

A)
B) 15
C) 25
D) 13

Question 23

Find the average value of the function f over the given region.

-f(x, y) = 10x + 7y over the region bounded by the coordinate axes and the lines and .

A) 73
B)
C)
D)

Question 24

Find the average value of the function f over the given region.

-f(x, y) = sin 3(x + y); R =

A)
B) 4
C)
D)

Question 25

Find the average value of the function f over the given region.

-f(x, y) = ; R =

A)
B)
C) 2e - 1
D) e - 1

Question 26

Find the average value of the function f over the given region.

-f(x, y) = ; R = {(x, y): 1 $\le$ x $\le$ 3, 1 $\le$ y $\le$ 3}

A)
B)
C)
D)

Question 27

Find the average value of the function f over the given region.

-f(x, y) = ; R = {(x, y): 1 $\le$ x $\le$ 5, 1 $\le$ y $\le$ 5}

A)
B)
C)
D)

Question 28

Find the average value of the function f over the given region.

-f(x, y) = over the region bounded by , , , and .

A) ln 2
B) ln 2
C) ln 2
D) 56 ln 2

Question 29

Find the average value of the function f over the given region.

-f(x, y) = over the region bounded by , , , and .

A) e - 1
B)
C) 2e - 1
D)

Question 30

Solve the problem.

-The northern third of Indiana is a rectangle measuring 96 miles by 132 miles. Thus, let Assuming that the total annual snowfall (in inches), S(x,y), at is given by the function S(x,y) = 60 with (x,y) D, find the average snowfall on D.

A)52.06 inches
B) 52.44 inches
C)51.78 inches
D) 51.14 inches

Question 31

Solve the problem.

-If f(x, y) = ( 3000 )/(1 + /2) represents the population density of a planar region on Earth, where x and y are measured in miles, find the number of people within the rectangle -7 $\le$ x $\le$ 7 and -3 $\le$ y $\le$ 0.

A)
B)
C)
D)

Question 32

Find the volume under the surface z = f(x,y) and above the rectangle with the given boundaries.

-z = 6 y; R = {(x, y): 0 $\le$ x $\le$ 4, 0 $\le$ y $\le$ 3}

A) 576
B) 1256
C) 2256
D) 676

Question 33

Find the volume under the surface z = f(x,y) and above the rectangle with the given boundaries.

-z = + ; R = {(x, y): 0 $\le$ x $\le$ 1, 0 $\le$ y $\le$ 1}

A)
B)
C)
D)

Question 34

Find the volume under the surface z = f(x,y) and above the rectangle with the given boundaries.

-z = 8x + 4y + 7; R = {(x, y): 0 $\le$ x $\le$ 1, 1 $\le$ y $\le$ 3}

A) 28
B) 26
C) 36
D) 38

Question 35

Find the volume under the surface z = f(x,y) and above the rectangle with the given boundaries.

-z = 4 + 9 ; R = {(x, y): 0 $\le$ x $\le$ 1, 0 $\le$ y $\le$ 1}

A)
B)
C)
D)

Question 36

Find the volume under the surface z = f(x,y) and above the rectangle with the given boundaries.

-z = ; R = {(x, y): 0 $\le$ x $\le$ 1, 1 $\le$ y $\le$ e}

A)
B)
C)
D)

Question 37

Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral.

-The coordinate axes and the line

A)
B)
C)
D)

Question 38

Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral.

-The coordinate axes and the line

A)
B)
C)
D)

Question 39

Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral.

-The lines , , and

A)
B)
C)
D)

Question 40

Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral.

-The parabola and the line

A)
B)
C)
D)

Question 41

Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral.

-The curve and the lines and

A)
B)
C)
D)

Question 42

Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral.

-The parabola and the line

A)
B)
C)
D)

Question 43

Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral.

-The curve and the lines and

A)
B)
C)
D)

Question 44

Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral.

-The lines , , and

A)
B)
C)
D)

Question 45

Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral.

-The lines , , and

A)
B)
C)
D)

Question 46

Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral.

-The curves and

A)
B)
C)
D)

Question 47

Evaluate the integral.

-

A) 3
B) -
C)
D) -1

Question 48

Evaluate the integral.

-

A) 27
B) 9
C)
D)

Question 49

Evaluate the integral.

-

A)
B)
C)
D)

Question 50

Evaluate the integral.

-

A)
B)
C)
D)

Question 51

Evaluate the integral.

-

A)
B)
C)
D)

Question 52

Evaluate the integral.

-

A) 16
B) 50
C) 32
D) 25

Question 53

Evaluate the integral.

-

A)
B)
C)
D)

Question 54

Evaluate the integral.

-

A)
B)
C)
D)

Question 55

Evaluate the integral.

-

A) (e - 1) ²
B) (e - 1) ²
C)
D)

Question 56

Integrate the function f over the given region.

-f(x, y) = xy over the triangular region with vertices (0, 0), ( 5, 0), and (0, 8)

A)
B)
C)
D)

Question 57

Integrate the function f over the given region.

-f(x, y) = + over the trapezoidal region bounded by the x-axis, y-axis, line and line

A)
B)
C)
D)

Question 58

Integrate the function f over the given region.

-f(x, y) = over the region bounded by the x-axis, line and curve

A) 7
B) 1
C) 8
D) 9

Question 59

Integrate the function f over the given region.

-f(x, y) = over the region bounded by the x-axis, line and curve

A) 8
B) 1
C) 7
D) 9

Question 60

Find the volume of the indicated region.

-the region that lies under the paraboloid and above the triangle enclosed by the lines , and

A)
B) 8505
C) 76,545
D) 945

Question 61

Find the volume of the indicated region.

-the tetrahedron bounded by the coordinate planes and the plane

A) 18
B) 27
C) 54
D) 36

Question 62

Find the volume of the indicated region.

-the region that lies under the plane and above the square

A)
B)
C)
D)

Question 63

Find the volume of the indicated region.

-the solid cut from the first octant by the surface

A)
B)
C)
D)

Question 64

Find the volume of the indicated region.

-the region under the surface , and bounded by the planes and and the cylinder

A)
B)
C)
D)

Question 65

Find the volume of the indicated region.

-the region bounded by the paraboloid and the xy-plane

A) 64 $\pi$
B) 128 $\pi$
C) $\pi$
D) $\pi$

Question 66

Find the volume of the indicated region.

-the region bounded by the paraboloid and the plane

A) $\pi$
B) 64 $\pi$
C) 128 $\pi$
D) $\pi$

Question 67

Find the volume of the indicated region.

-the region bounded by the paraboloid , the cylinder , and the

A) $\pi$
B) 5000 $\pi$
C) $\pi$
D) 2500 $\pi$

Question 68

Find the volume of the indicated region.

-the region that lies under the plane and over the triangle with vertices at , , and

A) 8
B)
C) 4
D)

Question 69

Find the volume of the indicated region.

-the region that lies under the plane and over the triangle bounded by the lines , , and

A) 50
B) 64
C) 56
D) 70

Question 70

Write an equivalent double integral with the order of integration reversed.

-

A)
B)
C)
D)

Question 71

Write an equivalent double integral with the order of integration reversed.

-

A)
B)
C)
D)

Question 72

Write an equivalent double integral with the order of integration reversed.

-

A)
B)
C)
D)

Question 73

Write an equivalent double integral with the order of integration reversed.

-

A)
B)
C)
D)

Question 74

Write an equivalent double integral with the order of integration reversed.

-

A)
B)
C)
D)

Question 75

Write an equivalent double integral with the order of integration reversed.

-

A)
B)
C)
D)

Question 76

Write an equivalent double integral with the order of integration reversed.

-

A)
B)
C)
D)

Question 77

Write an equivalent double integral with the order of integration reversed.

-

A)
B)
C)
D)

Question 78

Write an equivalent double integral with the order of integration reversed.

-

A)
B)
C)
D)

Question 79

Write an equivalent double integral with the order of integration reversed.

-

A)
B)
C)
D)

Question 80

Reverse the order of integration and then evaluate the integral.

-

A) 1 - cos 5
B) - cos 5
C) cos 5
D) 1 + cos 5