16 MULTIPLE INTEGRALS

GROUP WORK 2, SECTION 16.1
An Odd Function (Version 2)
In this exercise, we are going to try to approximate the double integral ∫∫ (
[−2,2] × [−2,2] x 3 + y 5) dA. We
start by partitioning the region [−2, 2] × [−2, 2] into four smaller regions, then nine, then sixteen, like this:
Now we approximate the double integral as discussed in the text, picking one point in every smaller region.
To make things simple, just choose the upper right corner of every small region, like so:
Approximation for four regions:
Approximation for nine regions:
Approximation for sixteen regions:
When you are finished, try again using a point of your choice in each region.
Using Arbitrarily Chosen Points
Approximation for four regions:
Approximation for nine regions:
Approximation for sixteen regions:
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