Chapter 4 Integration.

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Presentation transcript:

Chapter 4 Integration

Definition of an Antiderivative Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 4.1 Representation of Antiderivatives Copyright © Houghton Mifflin Company. All rights reserved.

Basic Integration Rules Copyright © Houghton Mifflin Company. All rights reserved.

Sigma Notation Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 4.2 Summation Formulas Copyright © Houghton Mifflin Company. All rights reserved.

Figure 4.5 Copyright © Houghton Mifflin Company. All rights reserved.

Figure 4.6 Copyright © Houghton Mifflin Company. All rights reserved.

Figure 4.7 Copyright © Houghton Mifflin Company. All rights reserved.

Figure 4.8 Copyright © Houghton Mifflin Company. All rights reserved.

Figure 4.10 Copyright © Houghton Mifflin Company. All rights reserved.

Figure 4.11 Copyright © Houghton Mifflin Company. All rights reserved.

Figure 4.12 Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 4.3 Limits of the Lower and Upper Sums Copyright © Houghton Mifflin Company. All rights reserved.

Definition of the Area of a Region in the Plane Copyright © Houghton Mifflin Company. All rights reserved.

Definition of a Riemann Sum Copyright © Houghton Mifflin Company. All rights reserved.

Definition of a Definite Integral Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 4.4 Continuity Implies Integrability Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 4.5 The Definite Integral as the Area of a Region Copyright © Houghton Mifflin Company. All rights reserved.

Definitions of Two Special Definite Integrals Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 4.6 Additive Interval Property Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 4.7 Properties of Definite Integrals Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 4.8 Preservation of Inequality Copyright © Houghton Mifflin Company. All rights reserved.

Figure 4.27 Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 4.9 The Fundamental Theorem of Calculus Copyright © Houghton Mifflin Company. All rights reserved.

Guidelines for Using the Fundamental Theorem of Calculus Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 4.10 Mean Value Theorem for Integrals and Figure 4.30 Copyright © Houghton Mifflin Company. All rights reserved.

Definition of the Average Value of a Function on an Interval and Figure 4.32 Copyright © Houghton Mifflin Company. All rights reserved.

Definite Integral diagrams Copyright © Houghton Mifflin Company. All rights reserved.

Figure 4.35 Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 4.11 The Second Fundamental Theorem of Calculus Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 4.12 Antidifferentiation of a Composite Function Copyright © Houghton Mifflin Company. All rights reserved.

Guidelines for Making a Change of Variables Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 4.13 The General Power Rule for Integration Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 4.14 Change of Variables for Definite Integrals Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 4.15 Integraion of Even and Odd Functions and Figure 4.39 Copyright © Houghton Mifflin Company. All rights reserved.

Figure 4.41 Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 4.16 The Trapezoidal Rule Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 4.17 Integral of p(x) =Ax2 + Bx + C Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 4.18 Simpson's Rule (n is even) Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 4.19 Errors in the Trapezoidal Rule and Simpson's Rule Copyright © Houghton Mifflin Company. All rights reserved.