# College Math Teaching

## October 16, 2013

### Convincing calculus students that the symbols MEAN SOMETHING

Filed under: applications of calculus, calculus, integrals — collegemathteaching @ 12:04 am

On a recent exam, the first 5 questions were as follows:

Given the region bounded by $x = \frac{1}{2}, x = 1, y = 0, y = \frac{1}{x}$

1. Find the AREA enclosed by the region.

2. Find the volume obtained by revolving this area about the $y$ axis (the line $x = 0$).

3. Find the volume obtained by revolving this area about the $x$ axis (the line $y = 0$).

4. Find $\bar{x}$. (constant density lamina).

5. Find $\bar{y}$.

Many students did fine, though there were a couple who literally blanked out on how to integrate $\frac{1}{x}$.

But some…well expect a few errors. But there were some who put a factor of $\pi$ 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.