1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 1

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Chapter 7 Applications of Definite Integrals

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 7.1 Integral As Net Change

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 4 Quick Review

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 5 Quick Review Solutions

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 6 What you’ll learn about Linear Motion Revisited General Strategy Consumption Over Time Net Change from Data Work …and why The integral is a tool that can be used to calculate net change and total accumulation.

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 7 Example Linear Motion Revisited

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 8 Example Linear Motion Revisited

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 9 Strategy for Modeling with Integrals

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 10 Example Potato Consumption

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 11 Example Potato Consumption

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 12 Work

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 13 Hooke’s Law

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 14 Example A Bit of Work

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 15 Example A Bit of Work

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 7.2 Areas in the Plane

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 17 Quick Review

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 18 Quick Review Solutions

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 19 What you’ll learn about Area Between Curves Area Enclosed by Intersecting Curves Boundaries with Changing Functions Integrating with Respect to y Saving Time with Geometric Formulas …and why The techniques of this section allow us to compute areas of complex regions of the plane.

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 20 Area Between Curves

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 21 Area Between Curves

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 22 Example Applying the Definition

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 23 Example Area of an Enclosed Region

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 24 Integrating with Respect to y

25. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 25 Example Integrating with Respect to y

26. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 26 Example Using Geometry

27. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 7.3 Volumes

28. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 28 Quick Review

29. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 29 Quick Review Solutions

30. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 30 What you’ll learn about Volumes As an Integral Square Cross Sections Circular Cross Sections Cylindrical Shells Other Cross Sections …and why The techniques of this section allow us to compute volumes of certain solids in three dimensions.

31. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 31 Volume of a Solid

32. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 32 How to Find Volumes by the Method of Slicing

33. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 33 Example Square Cross Sections

34. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 34 Example Square Cross Sections

35. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 35 Example A Solid of Revolution

36. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 36 Example Finding Volumes Using Cylindrical Shells

37. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 37 Example Finding Volumes Using Cylindrical Shells

38. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 38 Example Finding Volumes Using Cylindrical Shells

39. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 39 Example Finding Volumes Using Cylindrical Shells

40. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 40 Example Other Cross Sections

41. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 41 Example Other Cross Sections

42. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 42 Quick Quiz Sections 7.1-7.3

43. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 43 Quick Quiz Sections 7.1-7.3

44. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 44 Quick Quiz Sections 7.1-7.3

45. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 45 Quick Quiz Sections 7.1-7.3

46. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 46 Quick Quiz Sections 7.1-7.3

47. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 47 Quick Quiz Sections 7.1-7.3

48. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 7.4 Lengths of Curves

49. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 49 Quick Review

50. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 50 Quick Review Solutions

51. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 51 What you’ll learn about A Sine Wave Length of a Smooth Curve Vertical Tangents, Corners, and Cusps …and why The length of a smooth curve can be found using a definite integral.

52. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 52 Example The Length of a Sine Wave

53. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 53 Example The Length of a Sine Wave

54. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 54 Arc Length: Length of a Smooth Curve

55. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 55 Example Applying the Definition

56. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 56 Example A Vertical Tangent

57. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 57 Example Getting Around a Corner

58. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 7.5 Applications from Science and Statistics

59. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 59 Quick Review

60. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 60 Quick Review Solutions

61. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 61 What you’ll learn about Work Revisited Fluid Force and Fluid Pressure Normal Probabilities …and why It is important to see applications of integrals as various accumulation functions

62. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 62 Example Finding the Work Done by a Force

63. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 63 Example Work Done Lifting

64. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 64 Example Work Done Lifting

65. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 65 Example Work Done Lifting

66. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 66 Fluid Force and Fluid Pressure

67. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 67 Example The Great Molasses Flood if 1919 At 1:00 pm on January 15, 1919, a 90-ft-high, 90-foot-diameter cylindrical metal tank in which the Puritan Distilling Company stored molasses at the corner of Foster and Commercial streets in Boston’s North End exploded. Molasses flooded the streets 30 feet deep, trapping pedestrians and horses, knocking down buildings and oozing into homes. It was eventually tracked all over town and even made its way into the suburbs via trolley cars and people’s shoes. It took weeks to clean up. (a) Given that the tank was full of molasses weighing 100 lb/ft 3, what was the total force exerted by the molasses on the bottom of the tank at the time it ruptured? (b) What was the total force against the bottom foot-wide band of the tank wall?

68. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 68 Example The Great Molasses Flood if 1919

69. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 69 Example The Great Molasses Flood if 1919

70. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 70 Probability Density Function (pdf)

71. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 71 Normal Probability Density Function (pdf)

72. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 72 The 68-95-99.7 Rule for Normal Distributions

73. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 73 Example A Telephone Help Line Suppose a telephone help line takes a mean of 1.5 minutes to answer a call. If the standard deviation is 0.2, then 68% of the calls are answered in the range of 1.3 to 1.7 minutes and 99.7% of the calls are answered in the range of 0.9 to 2.1 minutes.

74. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 74 Example Weights of Coffee Cans

75. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 75 Example Weights of Coffee Cans

76. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 76 Quick Quiz Sections 7.4 and 7.5

77. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 77 Quick Quiz Sections 7.4 and 7.5

78. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 78 Quick Quiz Sections 7.4 and 7.5

79. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 79 Quick Quiz Sections 7.4 and 7.5

80. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 80 Quick Quiz Sections 7.4 and 7.5

81. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 81 Quick Quiz Sections 7.4 and 7.5

82. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 82 Chapter Test

83. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 83 Chapter Test

84. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 84 Chapter Test

85. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 85 Chapter Test

86. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 86 Chapter Test

87. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 87 Chapter Test Solutions

88. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 88 Chapter Test Solutions

89. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 89 Chapter Test Solutions

90. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 90 Chapter Test Solutions