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Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 13 Multiple Integration.

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Presentation on theme: "Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 13 Multiple Integration."— Presentation transcript:

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2 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 13 Multiple Integration

3 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 13.1 Double Integrals over Rectangular Regions

4 Slide 13 - 4 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

5 Slide 13 - 5 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

6 Slide 13 - 6 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

7 Slide 13 - 7 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

8 Slide 13 - 8 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

9 Slide 13 - 9 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

10 Slide 13 - 10 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

11 Slide 13 - 11 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

12 Slide 13 - 12 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

13 Slide 13 - 13 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

14 Slide 13 - 14 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

15 Slide 13 - 15 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

16 Slide 13 - 16 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

17 13.2 Double Integrals over General Regions

18 Slide 13 - 18 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

19 Slide 13 - 19 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

20 Slide 13 - 20 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

21 Slide 13 - 21 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

22 Slide 13 - 22 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

23 Slide 13 - 23 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

24 Slide 13 - 24 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

25 Slide 13 - 25 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

26 Slide 13 - 26 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

27 Slide 13 - 27 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

28 Slide 13 - 28 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

29 Slide 13 - 29 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

30 Slide 13 - 30 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

31 Slide 13 - 31 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

32 Slide 13 - 32 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

33 Slide 13 - 33 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

34 Slide 13 - 34 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

35 Slide 13 - 35 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

36 Slide 13 - 36 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

37 13.3 Double Integrals in Polar Coordinates

38 Slide 13 - 38 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

39 Slide 13 - 39 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

40 Slide 13 - 40 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

41 Slide 13 - 41 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

42 Slide 13 - 42 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

43 Slide 13 - 43 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

44 Slide 13 - 44 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

45 Slide 13 - 45 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

46 Slide 13 - 46 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

47 Slide 13 - 47 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

48 Slide 13 - 48 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

49 Slide 13 - 49 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

50 13.4 Triple Integrals

51 Slide 13 - 51 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

52 Slide 13 - 52 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

53 Slide 13 - 53 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

54 Slide 13 - 54 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

55 Slide 13 - 55 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

56 Slide 13 - 56 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

57 Slide 13 - 57 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

58 Slide 13 - 58 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

59 Slide 13 - 59 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

60 Slide 13 - 60 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

61 Slide 13 - 61 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

62 Slide 13 - 62 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

63 Slide 13 - 63 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

64 Slide 13 - 64 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

65 13.5 Triple Integrals in Cylindrical and Spherical Coordinates

66 Slide 13 - 66 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

67 Slide 13 - 67 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

68 Slide 13 - 68 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

69 Slide 13 - 69 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

70 Slide 13 - 70 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

71 Slide 13 - 71 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

72 Slide 13 - 72 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

73 Slide 13 - 73 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

74 Slide 13 - 74 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

75 Slide 13 - 75 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

76 Slide 13 - 76 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

77 Slide 13 - 77 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

78 Slide 13 - 78 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

79 Slide 13 - 79 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

80 Slide 13 - 80 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

81 Slide 13 - 81 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

82 Slide 13 - 82 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

83 Slide 13 - 83 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

84 Slide 13 - 84 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

85 Slide 13 - 85 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

86 Slide 13 - 86 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

87 Slide 13 - 87 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

88 Slide 13 - 88 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

89 Slide 13 - 89 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

90 13.6 Integrals for Mass Calculations

91 Slide 13 - 91 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

92 Slide 13 - 92 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

93 Slide 13 - 93 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

94 Slide 13 - 94 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

95 Slide 13 - 95 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

96 Slide 13 - 96 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

97 Slide 13 - 97 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

98 Slide 13 - 98 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

99 Slide 13 - 99 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

100 Slide 13 - 100 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

101 Slide 13 - 101 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

102 Slide 13 - 102 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

103 Slide 13 - 103 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

104 Slide 13 - 104 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

105 Slide 13 - 105 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

106 Slide 13 - 106 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

107 13.7 Change of Variables in Multiple Integrals

108 Slide 13 - 108 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

109 Slide 13 - 109 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

110 Slide 13 - 110 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

111 Slide 13 - 111 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

112 Slide 13 - 112 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

113 Slide 13 - 113 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

114 Slide 13 - 114 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

115 Slide 13 - 115 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

116 Slide 13 - 116 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

117 Slide 13 - 117 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

118 Slide 13 - 118 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

119 Slide 13 - 119 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

120 Slide 13 - 120 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

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122 Slide 13 - 122 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

123 Slide 13 - 123 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley


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