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

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Presentation on theme: "Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Definite Integrals Section 5.2."— Presentation transcript:

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

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

3 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 3 Sigma Notation

4 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 4

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

6 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 6 The Existence of Definite Integrals

7 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 7 The Definite Integral of a Continuous Function on [a,b]

8 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 8 The Definite Integral

9 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 9 Example Using the Notation

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

11 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example: Revisiting Area Under a Curve Evaluate the integral Slide Visual

12 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Area

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

14 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall A train moves along a track at a steady rate of 75 miles per hour from 7:00 AM to 9:00 AM. Express its total distance traveled as an integral, then evaluate the integral. Slide 5- 14

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

16 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Discontinuous Integrable Functions Slide 5- 16

17 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Pages (1, 5, 9, 11, 15, 23, 39, 41) Slide 5- 17


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