On a recent exam, the first 5 questions were as follows:
Given the region bounded by
1. Find the AREA enclosed by the region.
2. Find the volume obtained by revolving this area about the axis (the line ).
3. Find the volume obtained by revolving this area about the axis (the line ).
4. Find . (constant density lamina).
5. Find .
Many students did fine, though there were a couple who literally blanked out on how to integrate .
But some…well expect a few errors. But there were some who put a factor of in their answers to 4, 5, and…yes, even 1.
Evidently, I’ll have to give my “these symbols actually have MEANING” speech again.
Note: yes, there were some interesting symmetries here; perhaps some students didn’t believe their answers.