| Section | You should be able to… | Example | Review Exercises |
|---|---|---|---|
| 6.1 | 1 Find the area between the graphs of two functions by partitioning the \(x\)-axis (p.405) | 1-4 | 1-5, 21 |
| 2 Find the area between the graphs of two functions by partitioning the \(y\)-axis (p.408) | 5-7 | 3, 4, 21 | |
| 6.2 | 1 Use the disk method to find the volume of a solid formed by revolving a region about the \(x\)-axis (p. 415) | 1, 2 | 9, 11 |
| 2 Use the disk method to find the volume of a solid formed by revolving a region about the \(y\)-axis (p.416) | 3 | 8 | |
| 3 Use the washer method to find the volume of a solid formed by revolving a region about the \(x\)-axis (p.418) | 4 | 6, 14, 38(a) | |
| 4 Use the washer method to find the volume of a solid formed by revolving a region about the \(y\)-axis (p.420) | 5 | 13, 38(b) | |
| 5 Find the volume of a solid formed by revolving a region about a line parallel to a coordinate axis (p.421) | 6, 7 | 10, 12, 15, 38(c), (d) | |
| 6.3 | 1 Use the shell method to find the volume of a solid formed by revolving a region about the \(y\)-axis (p.425) | 1, 2 | 7, 8, 13, 38(b) |
| 2 Use the shell method to find the volume of a solid formed by revolving a region about the \(x\)-axis (p.428) | 3 | 9, 23 | |
| 3 Use the shell method to find the volume of a solid formed by revolving a region about a line parallel to a coordinate axis (p.430) | 4 | 12, 15, 38(e), (f) | |
| 6.4 | 1 Use the slicing method to find the volume of a solid (p.433) | 1-4 | 22, 24, 25 |
| 6.5 | 1 Find the arc length of the graph of a function \(y=f(x) \) (p.439) | 1, 2 | 16, 17, 26 |
| 2 Find the arc length of the graph of a function using a partition of the \(y\)-axis (p.441) | 3 | 18 | |
| 6.6 | 1 Find the work done by a variable force (p.445) | 1 | 27, 28 |
| 2 Find the work done by a spring force (p.446) | 2, 3 | 30, 31 | |
| 3 Find the work done to pump liquid (p.448) | 4, 5 | 29 | |
| 6.7 | 1 Find hydrostatic pressure and force (p.453) | 1, 2 | 32-34 |
| 6.8 | 1 Find the center of mass of a finite system of objects (p.458) | 1, 2 | 19, 20 |
| 2 Find the centroid of a homogeneous lamina (p.460) | 3-5 | 35 | 3 Find the volume of a solid of revolution using the Pappus Theorem (p.464) | 6 | 36, 37 |