1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Trapezoidal Rule Section 5.5

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 2 What you’ll learn about Trapezoidal Approximations Other Algorithms Error Analysis … and why Some definite integrals are best found by numerical approximations, and rectangles are not always the most efficient figures to use.

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

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

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Use the Trapezoidal Rule with n = 4 to estimate. Compare the estimate with the value of NINT and with the exact value. Slide 5- 5

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall An observer measures the outside temperature every hour from noon until midnight, recording the temperatures in the following table. What was the average temperature for the 12-hour period? Slide 5- 6 Time N1234567891011M Tem 63656668706968 6564625855

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 7 Simpson’s Rule

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Use Simpson’s Rule with n = 4 to approximate Slide 5- 8

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Pages 295-296 (1-7 odd) Slide 5- 9