5 Antidifferentiation
A. Antiderivatives
B. Basic Formulas
C. Integration by Partial Fractions BC ONLY
D. Integration by Parts BC ONLY
E. Applications of Antiderivatives; Differential Equations
Practice Exercises
6 Definite Integrals
A. Fundamental Theorem of Calculus (FTC); Definition of Definite Integral
B. Properties of Definite Integrals
C. Integrals Involving Parametrically Defined Functions BC ONLY
D. Definition of Definite Integral as the Limit of a Sum: The Fundamental Theorem Again BC
ONLY
E. Approximations of the Definite Integral; Riemann Sums
E1. Using Rectangles
E2. Using Trapezoids
Comparing Approximating Sums
Graphing a Function from Its Derivative; Another Look
F. Interpreting ln x as an Area
G. Average Value
Practice Exercises
7 Applications of Integration to Geometry
A. Area
A1. Area Between Curves
A2. Using Symmetry
B. Volume
B1. Solids with Known Cross Sections
B2. Solids of Revolution
C. Arc Length BC ONLY
D. Improper Integrals BC ONLY
Practice Exercises
8 Further Applications of Integration
A. Motion Along a Straight Line
B. Motion Along a Plane Curve BC ONLY
C. Other Applications of Riemann Sums
D. FTC: Definite Integral of a Rate Is Net Change
Practice Exercises
