Deck 15: Multiple Integrals

Question 1

Answer 1

Question 2

Answer 2

Question 3

Answer 3

Question 4

Find the center of mass of the lamina of the region shown if the density of the circular lamina is
four times that of the rectangular lamina.

Question 5

Question 6

Question 7

Question 8

Question 9

Calculate the iterated integral.

Question 10

Calculate the iterated integral.

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Evaluate the integral by changing to polar coordinates.

Question 18

Question 19

Describe the region whose area is given by the integral.

Question 20

Calculate the iterated integral.

Question 21

Question 22

Calculate the double integral.

Question 23

Calculate the iterated integral.

Question 24

Use cylindrical coordinates to evaluate the triple integral

Question 25

Calculate the iterated integral.

Question 26

Question 27

Question 28

Evaluate the iterated integral by converting to polar coordinates.Round the answer to two decimal places.

Question 29

Question 30

Evaluate the iterated integral.

Question 31

Question 32

Use the Midpoint Rule with four squares of equal size to estimate the double integral.

Question 33

Evaluate the double integral by first identifying it as the volume of a solid.

Question 34

Find the Jacobian of the transformation.

Question 35

Question 36

Question 37

Question 38

Question 39

Question 40

Question 41

Evaluate the double integral by first identifying it as the volume of a solid.

Question 42

Question 43

Question 44

Question 45

Question 46

Evaluate the iterated integral.

Question 47

Question 48

Calculate the double integral.

Question 49

Question 50

Use spherical coordinates.

Question 51

Question 52

Question 53

Question 54

Question 55

Question 56

Question 57

Calculate the iterated integral.Round your answer to two decimal places.

Question 58

Question 59

Question 60

Use cylindrical coordinates to evaluate the triple integral