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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.

==== Props/Equipment ====

  * [[:Props:start#whiteboards|Tabletop Whiteboard]] with markers
  * A handout for each student

==== 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 ====

(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
[[courses:activities:mvact:mvtriangle|Triangle]] and
[[courses:activities:mvact:mvdouble|Double Integral]] activities instead of
this one, or possibly just after this one.