ABC: Approach to the Basics of Calculus (Integration)

In the chapter Integration you will find:

1. Area as a Limit of Sums
2. The Definite Integral
3. Properties of Integrals
4. Methods of Integration
5. Substitutions
6. Partial Fractions
7. Improper Integrals
8. Volumes of Solids
9. Arc Length
10. Area of a Surface of Revolution
11. Numerical Integration

Geometric idea behind the theory of integration is discussed. The definition and basic properties of Riemann’s integral are given. Basic integration formulas are provided along with more advanced methods for obtaining integrals of various elementary functions.

Learning outcomes

Student knows definitions of the area of a plane set and the Riemann integral. Student can give examples of functions that are Riemann integrable and of ones that are not. Student can apply standard integration methods, such as integration by parts and substitutions to obtain definite and indefinte intergals of elementary functions.