| Section | You should be able to … | Examples | Review Exercises |
|---|---|---|---|
| 5.1 | 1 Approximate the area under the graph of a function (p. 344) | 1, 2 | 1, 2 |
| 2 Find the area under the graph of a function (p. 348) | 3, 4 | 3, 4 | |
| 5.2 | 1 Define a definite integral as the limit of Riemann sums (p. 353) | 1, 2 | 5(a), (b) |
| 2 Find a definite integral using the limit of Riemann sums (p. 356) | 3–5 | 5(c) | |
| 5.3 | 1 Use Part 1 of the Fundamental Theorem of Calculus (p. 363) | 1–3 | 7-10, 52, 53 |
| 2 Use Part 2 of the Fundamental Theorem of Calculus (p. 365) | 4, 5 | 5(d), 11–13, 15–18, 56 | |
| 3 Interpret an integral using Part 2 of the Fundamental Theorem of Calculus (p. 365) | 6 | 6–21, 22, 57 | |
| 5.4 | 1 Use properties of the definite integral (p. 369) | 1–6 | 23, 24, 27, 28, 53 |
| 2 Work with the Mean Value Theorem for Integrals (p. 372) | 7 | 29, 30 | |
| 3 Find the average value of a function (p. 373) | 8 | 31–34 | |
| 5.5 | 1 Find indefinite integrals (p. 379) | 1 | 14 |
| 2 Use properties of indefinite integrals (p. 380) | 2, 3 | 19, 20, 35, 36 | |
| 3 Solve differential equations involving growth and decay (p. 382) | 4, 5 | 37, 38, 59, 60 | |
| 5.6 | 1 Find an indefinite integral using substitution (p. 387) | 1–5 | 39–41, 44, 45, 48, 51 |
| 2 Find a definite integral using substitution (p. 391) | 6, 7 | 42, 43, 46, 47, 50, 51, 54, 55, 49 | |
| 3 Integrate even and odd functions (p. 393) | 8, 9 | 25–26 | |
| 4 Solve differential equations: Newton's Law of Cooling (p. 394) | 10 | 58 |