AU Calculus Initiative

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Division of Mathematics and Computer Science
College of Liberal Arts and Sciences

Chapter 8: Area and the Definite Integral

In this chapter we will use Riemann sums to develop the notion of net area and the definite integral, then relate the definite and indefinite integral through the Fundamental Theorem of Calculus. We conclude the chapter by presenting the important integration technique of u-substitution and by using the TI-84 to study accumulated change.

8.1:	Sigma Notation and Summations

8.2:	The Definition of Net Area

8.3:	Rolle's Theorem and the Mean Value Theorem

8.4:	The Fundamental Theorem of Calculus (Part 1)

8.5:	The Fundamental Theorem of Calculus (Part 2)

8.6:	Integration by Substitution

8.7:	Modeling Accumulated Change with the TI-84

Chapter 8 Review

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This material is based upon work supported by the National Science Foundation under
Grant No. 1140437.

Any opinions, findings and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.