6 Definite Integrals
A. Fundamental Theorem of Calculus (FTC); Evaluation of Definite
Integral
B. Properties of Definite Integrals
C. Definition of Definite Integral as the Limit of a Riemann Sum
D. The Fundamental Theorem Again
E. Approximations of the Definite Integral; Riemann Sums
E1. Using Rectangles
E2. Using Trapezoids
E3. Comparing Approximating Sums
F. Graphing a Function from Its Derivative; Another Look
G. Interpreting ln x as an Area
H. 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
BC ONLY
C. Arc Length
BC ONLY
D. Improper Integrals
Practice Exercises
8 Further Applications of Integration
A. Motion Along a Straight Line