| Section(s) |
1. | Riemann Sums |
| a. |
Examples |
|
7.4, 7.5 |
| b. |
Sigma Notation | |
7.4 |
| c. |
Useful sums | |
7.4 |
| d. |
Limits of sums | |
7.5 |
|
2. | The Definite
Integral |
| a. |
Definition and notation | |
7.6, 7.5 |
| b. |
Interpretations | |
7.5 (sort of) |
| c. |
Sums, products and inequalities | |
7.6 |
| d. |
Integrability | |
7.6 |
|
3. | Antiderivatives |
| a. |
Definition and notation | |
7.2 |
| b. |
Uniqueness | |
7.2 |
| c. |
The Fundamental Theorem of Calculus | |
7.6 |
| d. |
The indefinite integral | |
7.2 |
|
4. | Integration Rules |
| a. |
Powers, sums | |
7.2 |
| b. |
Trigonometric rules | |
7.3 |
| c. |
Integration by substitution | |
7.3, 7.8 |
|
5. | Applications of Integration |
| a. |
Linear motion | |
7.7 |
| b. |
Area under a curve, signed area | |
7.5, 8.1 |
| c. |
Area between two curves | |
8.1 |
| d. |
Volumes of revolution | |
8.2, 8.3 |
| e. |
The Second Fundamental Theorem | |
7.6 |
|
6. | Logs and Exponents |
| a. |
Antiderivative of 1/x | |
4.4 |
| b. |
Properties of ln(x) | |
4.1, 4.4, 4.2 |
| c. |
Logarithmic differentiation | |
4.3 |
| d. |
Function inverses | |
4.1 |
| e. |
The exponential function | |
4.2, 4.4 |
| f. |
Properties of ex | |
4.1, 4.2, 4.4 |
| g. |
Loga and ax | |
4.2, 4.4 |
| h. |
Graphs of exponential and log functions | |
4.2 |
| i. |
Exponential growth | |
10.3 |
|
7. | Inverse Trigonometric Functions |
| a. |
Graphs, domains, ranges | |
4.5 |
| b. |
Triangle computations | |
4.5 |
| c. |
Derivatives | |
4.5 |
|
8. | More Integration Rules |
| a. |
Integrals resulting in inverse trig. functions | |
9.3 |
| b. |
Integration by parts | |
9.2 |
| c. |
Integrals of sin2(x) and cos2(x) | |
9.2 |
|
9. | Improper Integrals |
| a. |
Convergence and divergence | |
9.8 |
| b. |
Integrals over an infinite region | |
9.8 |
| c. |
Integrals over an open interval | |
9.8 |
|
10. | L'Hôpital's rule |
| a. |
Procedure | |
4.7 |
| b. |
Iterated procedure | |
4.7 |
| c. |
Other indeterminate forms | |
4.6 |