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.

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