Math 125: Week 4
| Week 3 outline | Math 125 main page | Week 5 outline |
| What | Where | Link |
|---|---|---|
| Reading | Text -- 6.2, 6.3 | |
| Worksheet | Website – Solids of Revolution | Astroid.pdf
(optional, on Tuesday) Worksheet 4 Solutions |
Student Guide:
Section 6.3 is either covered before the midterm, or it will be covered on the last lecture of the week on Friday. Section 6.3 presents an alternative method for computing volumes of solids of revolution, via subdividing them into concentric cylindrical "shells". This allows us to set up the Riemann Sums and thus the volume integrals in the opposite variable than the slicing disks/washers method, which can be important, depending on the situation.
It's important to master and be able to apply all methods for computing volumes and to understand that, depending on the region to be rotated and on the axis of revolution, one of the methods may be much better than the other. That is, you should be able to determine when it's best to integrate with respect to x or y, and when to use shells or washers.
This is the week of Midterm #1. Depending on the pacing of your instructor, the material covered on the first midterm will vary; it typically covers up to section 6.2 or 6.3, including. Ask your instructor for precise information on the sections covered. Keep these comments in mind as you look over old midterms in the archive. Some past quarters' midterm exams might include work problems; if your section has not covered section 6.4 before the midterm, skip such problems (for now). Many instructors devote one lecture period to an in-class review session, the day before the midterm.
WORKSHEET: The short worksheet Astroid.pdf may be given Tuesday, before the midterm, if both sections 6.2 and 6.3 have been covered by then. It provides a review of computing volumes of solids of revolution. It also introduces the astroid, a hypocycloid. Your instructor may choose to skip this worksheet.
| Week 3 outline | Math 125 main page | Week 5 outline |