Math 125: Week 4

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What Where Link
Reading Text – 6.3, 6.4
Worksheet    Website – Solids of Revolution Astroid.pdf
Worksheet 4 Solutions

Student Guide:

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 and may cover up to section 6.2 or 6.3 (or even 6.4.) Ask your instructor for precise information on the sections covered. Keep these comments in mind as you look over old midterms in the archive. The midterm will be given in TA section on Thursday. Many instructors devote one lecture period to an in-class review session, the day before the midterm.

The remaining lecture day this week is devoted to the application of integration to Work. While the concept of Work is important in Physics, the main thing to get here is yet another example of taking a problem and turning it into an integral. The more examples like this you see, the more likely it will be that you think of trying this in your own work.

  • 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.
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