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<title>
12.1 - Reading questions
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<h2>[12.1] - Reading Assignment
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<p>After reading sections 12.1

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<li>This question doesn't deal directly with integration but rather just asks to get acquainted (or re-acquainted) with the meaning of the double sum.  Calculate the value of this double sum:  (You should have six terms to add together...)
$$\sum_{i=1}^2\sum_{j=1}^3 2^i3^j=?$$
<p class="justme answer">
$$\begineq
\sum_{i=1}^2\sum_{j=1}^3 2^i3^j&=&2^13^1+2^13^2+2^13^3+2^23^1+2^23^2+2^23^3\\
  &=&6+18+54+12+36+108=234
\endeq$$
<li>
If we partition $[a, b]$ into $m$ subintervals of equal length and $[c, d]$ into $n$ subintervals of equal length, what is the area, $\Delta A$, for any subrectangle $R_{ij}$?
<p class="justme answer">All the sub-rectangles have the same area, $\Delta A$.  So if we divide the total area $A=(b-a)(c-d)$ by the number of sub-rectangles, which is $m*n$ we get:
$$\Delta A = \frac{A}{m*n}=\frac{(b-a)(c-d)}{m*n}=\frac{(b-a)}{m}\frac{(c-d)}{n}.$$
<br><img src="0g/12.1.read.jpg">

<li>Muddy questions? Questions you wonder about?</ol>
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