Deck 16: Multiple Integrals

Question 1

Evaluate the integral.

Answer 1

D

Question 2

Evaluate the double integral over the given region.

Answer 2

C

Question 3

Evaluate the integral.

Answer 3

B

Question 4

Evaluate the integral.

A) 36450
B) 4050
C) 675
D) 6075

Question 5

Evaluate the double integral over the given region.

Question 6

Evaluate the integral.

Question 7

Evaluate the double integral over the given region.

Question 8

Evaluate the integral.

Question 9

Evaluate the double integral over the given region.

Question 10

Evaluate the integral.

A) 14
B) -25
C) -5
D) 1

Question 11

Integrate the function f over the given region.

Question 12

Evaluate the double integral over the given region.

Question 13

Evaluate the integral.

A) 5
B) 480
C) 80
D) 30

Question 14

Evaluate the double integral over the given region.

Question 15

Evaluate the integral.

A) 27
B) 51
C) 33
D) 45

Question 16

Evaluate the integral.

A) - 10464
B) 8736
C) - 8736
D) 10464

Question 17

Evaluate the double integral over the given region.

Question 18

Evaluate the double integral over the given region.

A) 176
B) 528
C) 264
D) 352

Question 19

Evaluate the integral.

A) - 2730
B) - 2535
C) - 1170
D) 1365

Question 20

Evaluate the integral.

A) - 288
B) - 1152
C) - 2592
D) 288

Question 21

Evaluate the integral.

Question 22

Integrate the function f over the given region.

Question 23

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

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

Question 24

Evaluate the integral.

A) 9
B) 8
C) 4
D) 18

Question 25

Integrate the function f over the given region.

Question 26

Evaluate the integral.

Question 27

Integrate the function f over the given region.
f(x, y) = xy over the triangular region with vertices (0, 0), (5, 0), and (0, 10)

Question 28

Integrate the function f over the given region.

Question 29

Integrate the function f over the given region.

Question 30

Evaluate the integral.

Question 31

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

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

Question 32

Evaluate the integral.

Question 33

Evaluate the integral.

Question 34

Evaluate the integral.

Question 35

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

Question 36

Evaluate the integral.

Question 37

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

Question 38

Integrate the function f over the given region.

Question 39

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

Question 40

Evaluate the integral.

Question 41

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

Question 42

Integrate the function f over the given region.

Question 43

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

Question 44

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

Question 45

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

Question 46

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

Question 47

Reverse the order of integration and then evaluate the integral.

A) 9 cos 7
B) 9 sin 7
C) 7 sin 9
D) 7 cos 9

Question 48

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

Question 49

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

Question 50

Reverse the order of integration and then evaluate the integral.

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

Question 51

Integrate the function f over the given region.

Question 52

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

Question 53

Reverse the order of integration and then evaluate the integral.

Question 54

Reverse the order of integration and then evaluate the integral.

Question 55

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

Question 56

Reverse the order of integration and then evaluate the integral.

Question 57

Reverse the order of integration and then evaluate the integral.

Question 58

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

Question 59

Reverse the order of integration and then evaluate the integral.

A) 25
B) 35
C) 33
D) 27

Question 60

Integrate the function f over the given region.

A) 6
B) 1
C) 4
D) 5

Question 61

Find the volume of the indicated region.

Question 62

Find the volume of the indicated region.

Question 63

Evaluate the improper integral.

Question 64

Evaluate the improper integral.

Question 65

Evaluate the improper integral.

Question 66

Reverse the order of integration and then evaluate the integral.

Question 67

Reverse the order of integration and then evaluate the integral.

Question 68

Find the volume of the indicated region.

A) 240
B) 360
C) 180
D) 120

Question 69

Evaluate the improper integral.

A) 40
B) 240
C) 24
D) 360

Question 70

Find the volume of the indicated region.
the region that lies under the plane z = 5x + 3y and over the triangle bounded by the lines y = x, y = 2x, and x + y = 6

A) 40
B) 56
C) 50
D) 46

Question 71

Find the volume of the indicated region.

Question 72

Find the volume of the indicated region.

Question 73

Evaluate the improper integral.

Question 74

Evaluate the improper integral.

Question 75

Find the volume of the indicated region.

Question 76

Evaluate the improper integral.

Question 77

Find the volume of the indicated region.

Question 78

Find the volume of the indicated region.
the region that lies under the plane z = 6x + 9y and over the triangle with vertices at (1, 1), (2, 1), and (1, 2)

A) 16
B) 10
C) 20
D) 14

Question 79

Find the volume of the indicated region.

A) 72
B) 36
C) 8
D) 18

Question 80

Reverse the order of integration and then evaluate the integral.