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Merge pull request #83 from clark-archer/section-12.2-typos
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Fix some typos in section 12.2.
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bartsnapp committed Nov 9, 2013
2 parents 0302290 + b39716d commit f977681
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6 changes: 3 additions & 3 deletions public/textbook/integrals.tex
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Expand Up @@ -511,9 +511,9 @@ \section{Riemann Sums}
\end{tikzpicture}
\caption{A plot of $f(x)$ along with the partition
\[
[x_0,x_1]\cup [x_1, x_2]\cup [x_2,x_3]\cup [x_3,x_4]\cup[x_4,x_5] = [a,b]
[x_0,x_1]\cup [x_1, x_2]\cup [x_2,x_3]\cup [x_3,x_4] = [a,b]
\]
and the $y$-values $f(x_0^*)$, $f(x_1^*)$, $f(x_2^*)$, $f(x_3^*)$, $f(x_4^*)$.}
and the $y$-values $f(x_0^*)$, $f(x_1^*)$, $f(x_2^*)$, $f(x_3^*)$.}
\label{figure:areacompute2}
\end{marginfigure}
For each subinterval pick a point $x_i^*\in [x_i,x_{i+1}]$ and
Expand Down Expand Up @@ -626,7 +626,7 @@ \section{Riemann Sums}
where $x_i^*\in [x_i,x_{i+1}]$.
\end{definition}

There are actually at least five special Riemann sums, \textit{left},
There are actually at least five special Riemann sums: \textit{left},
\textit{right}, \textit{midpoint}, \textit{upper}, and \textit{lower}.

\begin{definition}
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