# Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 5.4 Fundamental Theorem of Calculus.

## Presentation on theme: "Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 5.4 Fundamental Theorem of Calculus."— Presentation transcript:

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- 2 Quick Review

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

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 4 What you’ll learn about Fundamental Theorem, Part 1 Graphing the Function Fundamental Theorem, Part 2 Area Connection Analyzing Antiderivatives Graphically … and why The Fundamental Theorem of Calculus is a Triumph of Mathematical Discovery and the key to solving many problems.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 5 The Fundamental Theorem of Calculus

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 6 The Fundamental Theorem of Calculus

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 7 Example Applying the Fundamental Theorem

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 8 Example The Fundamental Theorem with the Chain Rule

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 9 Example Variable Lower Limits of Integration

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 10 The Fundamental Theorem of Calculus, Part 2

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 11 The Fundamental Theorem of Calculus, Part 2

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 12 Example Evaluating an Integral

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 13 How to Find Total Area Analytically

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 14 How to Find Total Area Numerically

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

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 16 Quick Review

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 17 Quick Review Solutions

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

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 19 Trapezoidal Approximations

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

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 21 Simpson’s Rule

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 22 Error Bounds

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 23 Quick Quiz Sections 5.4 and 5.5 x1467 f(x)10304020

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 24 Quick Quiz Sections 5.4 and 5.5 x1467 f(x)10304020

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 25 Quick Quiz Sections 5.4 and 5.5

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 26 Quick Quiz Sections 5.4 and 5.5

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 27 Quick Quiz Sections 5.4 and 5.5

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 28 Quick Quiz Sections 5.4 and 5.5