16 MULTIPLE INTEGRALS
16 MULTIPLE INTEGRALS
16 MULTIPLE INTEGRALS
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GROUP WORK 2, SECTION <strong>16</strong>.1<br />
An Odd Function (Version 3)<br />
In this exercise, we are going to try to approximate the double integral ∫∫ (<br />
[−2,2] × [−2,2] x 3 + y 5) dA. We<br />
start by partitioning the region [−2, 2] × [−2, 2] into four smaller regions, then nine, then sixteen, like this:<br />
Now we approximate the double integral as discussed in the text, picking one point in every smaller region.<br />
To make things simple, just choose the midpoint of every small region, like so:<br />
Approximation for four regions:<br />
Approximation for nine regions:<br />
Approximation for sixteen regions:<br />
When you are finished, try again using a point of your choice in each region.<br />
Using Arbitrarily Chosen Points<br />
Approximation for four regions:<br />
Approximation for nine regions:<br />
Approximation for sixteen regions:<br />
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