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Chapter 4 Integration
Definition of an Antiderivative
Theorem 4.1 Representation of Antiderivatives
Basic Integration Rules
Sigma Notation
Theorem 4.2 Summation Formulas
Figure 4.5
Figure 4.6
Figure 4.7
Figure 4.8
Figure 4.10
Figure 4.11
Figure 4.12
Theorem 4.3 Limits of the Lower and Upper Sums
Definition of the Area of a Region in the Plane
Definition of a Riemann Sum
Definition of a Definite Integral
Theorem 4.4 Continuity Implies Integrability
Theorem 4.5 The Definite Integral as the Area of a Region
Definitions of Two Special Definite Integrals
Theorem 4.6 Additive Interval Property
Theorem 4.7 Properties of Definite Integrals
Theorem 4.8 Preservation of Inequality
Figure 4.27
Theorem 4.9 The Fundamental Theorem of Calculus
Guidelines for Using the Fundamental Theorem of Calculus
Theorem 4.10 Mean Value Theorem for Integrals and Figure 4.30
Definition of the Average Value of a Function on an Interval and Figure 4.32
Definite Integral diagrams
Figure 4.35
Theorem 4.11 The Second Fundamental Theorem of Calculus
Theorem 4.12 Antidifferentiation of a Composite Function
Guidelines for Making a Change of Variables
Theorem 4.13 The General Power Rule for Integration
Theorem 4.14 Change of Variables for Definite Integrals
Theorem 4.15 Integraion of Even and Odd Functions and Figure 4.39
Figure 4.41
Theorem 4.16 The Trapezoidal Rule
Theorem 4.17 Integral of p(x) =Ax2 + Bx + C
Theorem 4.18 Simpson's Rule (n is even)
Theorem 4.19 Errors in the Trapezoidal Rule and Simpson's Rule