Copyright © 2015, 2012, and 2009 Pearson Education, Inc. 1 Section 6.4 Fundamental Theorem of Calculus Applications of Derivatives Chapter 6.

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Presentation transcript:

Copyright © 2015, 2012, and 2009 Pearson Education, Inc. 1 Section 6.4 Fundamental Theorem of Calculus Applications of Derivatives Chapter 6

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 2 Quick Review

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 3 Quick Review Solutions

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 4 What you’ll learn about The Antiderivative Part of the Fundamental Theorem of Calculus Use of definite integrals to define new functions (accumulator functions) The Evaluation Part of the Fundamental Theorem of Calculus Evaluation of definite integrals using antiderivatives … and why The Fundamental Theorem of Calculus is a Triumph Of Mathematical Discovery and the key to solving many problems.

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 5 The Fundamental Theorem of Calculus

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 6 The Fundamental Theorem of Calculus

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 7 Example Applying the Fundamental Theorem

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 8 Example The Fundamental Theorem with the Chain Rule

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 9 Example Variable Lower Limits of Integration

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 10 The Fundamental Theorem of Calculus, Part 2

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 11 The Fundamental Theorem of Calculus, Part 2

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 12 Example Evaluating an Integral

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 13 How to Find Total Area Analytically

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 14 How to Find Total Area Numerically

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