1 Copyright © 2015, 2011 Pearson Education, Inc. Chapter 5 Integration.

Slides:



Advertisements
Similar presentations
Section 8.5 Riemann Sums and the Definite Integral.
Advertisements

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 1.
Copyright © 2008 Pearson Education, Inc. Chapter 9 Multivariable Calculus Copyright © 2008 Pearson Education, Inc.
Copyright © 2008 Pearson Education, Inc. Chapter 1 Linear Functions Copyright © 2008 Pearson Education, Inc.
Copyright © 2008 Pearson Education, Inc. Chapter 11 Probability and Calculus Copyright © 2008 Pearson Education, Inc.
Copyright © 2008 Pearson Education, Inc. Chapter 3 The Derivative Copyright © 2008 Pearson Education, Inc.
Copyright © 2008 Pearson Education, Inc. Chapter 7 Integration Copyright © 2008 Pearson Education, Inc.
Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Copyright © 2008 Pearson Education, Inc. Chapter 13 The Trigonometric Functions Copyright © 2008 Pearson Education, Inc.
© 2010 Pearson Education, Inc. All rights reserved.
Chapter 1 Introduction. Copyright © 2003 by Pearson Education, Inc.1-2.
Definite Integrals Finding areas using the Fundamental Theorem of Calculus.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 5.4 Fundamental Theorem of Calculus.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 1.
Section 5.3 – The Definite Integral
Chapter 4 Integration.
Copyright © 2008 Pearson Education, Inc. Chapter 8 Further Techniques and Applications of Integration Copyright © 2008 Pearson Education, Inc.
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved. MCS 122 Chapter 5 Review.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 5.1 Estimating with Finite Sums.
If a < b < c, then for any number b between a and c, the integral from a to c is the integral from a to b plus the integral from b to c. Theorem: Section.
Calculus, 8/E by Howard Anton, Irl Bivens, and Stephen Davis Copyright © 2005 by John Wiley & Sons, Inc. All rights reserved (p. 443) First Area.
Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 14 Vector Calculus.
Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley. Chapter 5 Integration.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 5 Integration.
Copyright © 2015, 2012, and 2009 Pearson Education, Inc. 1 Section 6.4 Fundamental Theorem of Calculus Applications of Derivatives Chapter 6.
Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 4.8 Antiderivatives.
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved. MCS 122 Chapter 5 Review.
Riemann Sums and the Definite Integral. represents the area between the curve 3/x and the x-axis from x = 4 to x = 8.
Section 4.3 Day 1 Riemann Sums and Definite Integrals AP Calculus BC.
Chapter Definite Integrals Obj: find area using definite integrals.
WS: Riemann Sums. TEST TOPICS: Area and Definite Integration Find area under a curve by the limit definition. Given a picture, set up an integral to calculate.
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved. Major theorems, figures,
Chapter 2 Opener © 2014 Pearson Education, Inc.. Figure 2.1 © 2014 Pearson Education, Inc.
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved. Major theorems, figures,
Definite Integral df. f continuous function on [a,b]. Divide [a,b] into n equal subintervals of width Let be a sample point. Then the definite integral.
Copyright (c) 2003 Brooks/Cole, a division of Thomson Learning, Inc. Integration 5 Antiderivatives Substitution Area Definite Integrals Applications.
Copyright © Cengage Learning. All rights reserved. 7 Techniques of Integration.
(MTH 250) Lecture 19 Calculus. Previous Lecture’s Summary Definite integrals Fundamental theorem of calculus Mean value theorem for integrals Fundamental.
Chapter 5 Accumulating Change: Limits of Sums and the Definite Integral.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Riemann Sums and the Definite Integral
Chapter 4 Opener © 2014 Pearson Education, Inc..
Chapter 11 Opener © 2014 Pearson Education, Inc..
Techniques of Integration
Approximating Definite Integrals. Left Hand Riemann Sums.
Approximating Definite Integrals. Left Hand Riemann Sums.
Chapter 5 Integrals.
Section 4.3 – Area and Definite Integrals
Copyright © 2006 Pearson Education, Inc
Chapter 4 Integration.
Chapter 5 Integration Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Chapter 7 MATH 1325 Business Calculus Ch.7 Copyright © 2005 Pearson Education, Inc.
Lesson 5-R Review of Chapter 5.
Chapter 3 MATH 1325 Business Calculus Ch.3 Copyright © 2005 Pearson Education, Inc.
Copyright © 2012, Elsevier Inc. All rights Reserved.
Chapter 5 MATH 1325 Business Calculus Ch.5 Copyright © 2005 Pearson Education, Inc.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Copyright © 2013 Elsevier Inc. All rights reserved.
Copyright © 2012, Elsevier Inc. All rights Reserved.
Chapter 7 Integration.
Copyright © 2012, Elsevier Inc. All rights Reserved.
Copyright © 2013 Elsevier Inc. All rights reserved.
Section 5.3 – The Definite Integral
Section 5.3 – The Definite Integral
Modeling Functionality with Use Cases
Copyright © 2012, Elsevier Inc. All rights Reserved.
Chapter 5 Integration.
Copyright © 2012, Elsevier Inc. All rights Reserved.
Copyright © 2013 Elsevier Inc. All rights reserved.
Copyright © 2012, Elsevier Inc. All rights Reserved.
Presentation transcript:

1 Copyright © 2015, 2011 Pearson Education, Inc. Chapter 5 Integration

2 Copyright © 2015, 2011 Pearson Education, Inc. 5.1 Approximating Areas under Curves

3 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.1

4 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.2

5 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.3

6 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.4 (a)

7 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.4 (b)

8 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.4 (c)

9 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.5

10 Copyright © 2015, 2011 Pearson Education, Inc. Table 5.1

11 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.6

12 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.7

13 Copyright © 2015, 2011 Pearson Education, Inc.

14 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.8

15 Copyright © 2015, 2011 Pearson Education, Inc.

16 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.9

17 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.10

18 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.11

19 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.12

20 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.13

21 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.14

22 Copyright © 2015, 2011 Pearson Education, Inc. Table 5.2

23 Copyright © 2015, 2011 Pearson Education, Inc.

24 Copyright © 2015, 2011 Pearson Education, Inc.

25 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.15

26 Copyright © 2015, 2011 Pearson Education, Inc. Table 5.3: Left, right, and midpoint Riemann sum approximations

27 Copyright © 2015, 2011 Pearson Education, Inc. 5.2 Definite Integrals

28 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.16

29 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.17

30 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.18

31 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.19

32 Copyright © 2015, 2011 Pearson Education, Inc.

33 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.20 (1 of 2)

34 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.20 (2 of 2)

35 Copyright © 2015, 2011 Pearson Education, Inc.

36 Copyright © 2015, 2011 Pearson Education, Inc.

37 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.21

38 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.22

39 Copyright © 2015, 2011 Pearson Education, Inc.

40 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.23

41 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.24

42 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.25

43 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.26

44 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.27

45 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.28

46 Copyright © 2015, 2011 Pearson Education, Inc.

47 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.29

48 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.30

49 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.31 (1 of 2)

50 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.31 (2 of 2)

51 Copyright © 2015, 2011 Pearson Education, Inc. Table 5.4

52 Copyright © 2015, 2011 Pearson Education, Inc. 5.3 Fundamental Theorem of Calculus

53 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.32

54 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.33

55 Copyright © 2015, 2011 Pearson Education, Inc.

56 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.34

57 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.35

58 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.36

59 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.37

60 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.38

61 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.39

62 Copyright © 2015, 2011 Pearson Education, Inc.

63 Copyright © 2015, 2011 Pearson Education, Inc.

64 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.40

65 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.41

66 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.42

67 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.43

68 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.44

69 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.45

70 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.46 (a)

71 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.46 (b & c)

72 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.46 (d & e)

73 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.47

74 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.48

75 Copyright © 2015, 2011 Pearson Education, Inc. 5.4 Working with Integrals

76 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.49 (a)

77 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.49 (b)

78 Copyright © 2015, 2011 Pearson Education, Inc.

79 Copyright © 2015, 2011 Pearson Education, Inc.

80 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.50

81 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.51

82 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.52

83 Copyright © 2015, 2011 Pearson Education, Inc.

84 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.53

85 Copyright © 2015, 2011 Pearson Education, Inc. 5.5 Substitution Rule

86 Copyright © 2015, 2011 Pearson Education, Inc.

87 Copyright © 2015, 2011 Pearson Education, Inc.

88 Copyright © 2015, 2011 Pearson Education, Inc.

89 Copyright © 2015, 2011 Pearson Education, Inc. Figure 5.54