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## Area: Instructor's Guide

### Main Ideas

• Integration involves chopping and adding.

Estimated Time: 15–30 minutes

Students work in groups to write down and evaluate single integrals for finding the area of a region bounded by 4 curves..

### Prerequisite Knowledge

• Single-variable integration.

### Activity: Introduction

This activity encourages students to think of integration as chopping and adding, emphasizing that there are many ways to chop.

(none yet)

### Activity: Wrap-up

Emphasize that integration is chopping and adding. If double integrals are explored, discuss the similarities differences between the corresponding single and double integrals.

### Extensions

If double integrals over rectangular regions have already been discussed, a natural extension would be to have students try to set up and evaluate double integrals for the area of the region. A further extension would be to introduce a density function $\sigma$ and evaluate $\int_R \sigma\,dA$ over the region, followed by a discussion of whether this integral could be computed as a single integral (which depends on the choice of $\sigma$).

An alternate choice for exploring such double integrals would be to use the Triangle and Double Integral activities instead of this one, or possibly just after this one.

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