- Assignment 7.8: graded 8, 29, 61
- Exam is this coming Monday, 11/15. Chapters 6 and 7.
- Tonight I'll stay after class until 10:00, if you want to do any extra problems in preparation for the upcoming exam.
- What kinds of problems are we looking at in this section? Arc
length and surface area calculations for areas of revolution:
- Let's start with arc length:
The usual trick is to discretize something continuous, and then pass to a limit:
Now hopefully we can figure out how the formula will look:
So what's the general formula?
- For surface area (for areas of revolution)
We discretize bits of the surface, and then make a series of little bands; take the limit, and get the general formula:
- Examples:
- #5, p. 475
- #12, p. 475
- #39, p. 476
- #51, p. 477