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Area: Instructor's Guide

Main Ideas

  • Integration involves chopping and adding.

Students' Task

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.

Activity: Student Conversations

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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.


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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