- Section 8.6 problems are due Thursday.
- I've fixed up your 8.1 problems (on-line):
- Q10 on-line: travelling 600 mph or so: how far do you go in an hour? Think about it. Use your head first, then do the math!
- Let's make sure that we have the basic numerical integration rules (such as Simpson's rule) set up properly in your calculators.
- #45, p. 465
- #98, p. 467 (see note preceeding exercise #96)
- 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