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11.1 mvh - Double integrals from data
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<h1>
[11.1] - Double integrals from data
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<p>Some of the values of the function $f(x,y)$ are given in the table below:<br>
<img src="0g/12.1.table.jpg"><br>
<p>Estimate 
$$\int_{y=80}^{100}\int_{x=20}^{60} f(x,y)\,dx\,dy\approx\sum_{i=1}^2\sum_{j=1}^2 f(x_{ij}^*,y_{ij}^*)\Delta x\Delta y$$
where $\Delta x=20$ and $\Delta y=10$. (That is, the 2 X 2  light overlay). Which point to use in each sub-rectangle?  Try:
<ol>
<li>midpoints
<br><br><br><br><br><br><br><br><br>
<li>points farthest away from the origin
<br><br><br><br><br><br><br><br><br>
</ol>