1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 5.1 Estimating with Finite Sums

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 2 Quick Review

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 3 Quick Review Solutions

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 4 What you’ll learn about Distance Traveled Rectangular Approximation Method (RAM) Volume of a Sphere Cardiac Output … and why Learning about estimating with finite sums sets the foundation for understanding integral calculus.

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 5 Example Finding Distance Traveled when Velocity Varies

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 6 Example Finding Distance Traveled when Velocity Varies

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 7 LRAM, MRAM, and RRAM approximations to the area under the graph of y=x 2 from x=0 to x=3

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 8 Example Estimating Area Under the Graph of a Nonnegative Function

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 5.2 Definite Integrals

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 10 Quick Review

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 11 Quick Review Solutions

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 12 What you’ll learn about Riemann Sums The Definite Integral Computing Definite Integrals on a Calculator Integrability … and why The definite integral is the basis of integral calculus, just as the derivative is the basis of differential calculus.

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 13 Sigma Notation

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 14 The Definite Integral as a Limit of Riemann Sums

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 15 The Existence of Definite Integrals

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 16 The Definite Integral of a Continuous Function on [a,b]

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 17 The Definite Integral

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 18 Example Using the Notation

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 19 Area Under a Curve (as a Definite Integral)

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 20 Area

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 21 The Integral of a Constant

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 22 Example Using NINT

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 5.3 Definite Integrals and Antiderivatives

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 24 Quick Review

25. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 25 Quick Review Solutions

26. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 26 What you’ll learn about Properties of Definite Integrals Average Value of a Function Mean Value Theorem for Definite Integrals Connecting Differential and Integral Calculus … and why Working with the properties of definite integrals helps us to understand better the definite integral. Connecting derivatives and definite integrals sets the stage for the Fundamental Theorem of Calculus.

27. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 27 Rules for Definite Integrals

28. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 28 Example Using the Rules for Definite Integrals

29. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 29 Example Using the Rules for Definite Integrals

30. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 30 Example Using the Rules for Definite Integrals

31. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 31 Average (Mean) Value

32. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 32 Example Applying the Definition

33. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 33 The Mean Value Theorem for Definite Integrals

34. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 34 The Mean Value Theorem for Definite Integrals

35. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 35 The Derivative of an Integral

36. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 36 Quick Quiz Sections 5.1 - 5.3

37. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 37 Quick Quiz Sections 5.1 - 5.3

38. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 38 Quick Quiz Sections 5.1 - 5.3

39. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 39 Quick Quiz Sections 5.1 - 5.3

40. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 40 Quick Quiz Sections 5.1 - 5.3

41. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 41 Quick Quiz Sections 5.1 - 5.3