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%%
%% An UIT Edition example
%%
%% Example 09-17-13 on page 193.
%%
%% Copyright (C) 2010 Herbert Voss
%%
%% It may be distributed and/or modified under the conditions
%% of the LaTeX Project Public License, either version 1.3
%% of this license or (at your option) any later version.
%%
%% See http://www.latex-project.org/lppl.txt for details.
%%
%%
%% ====
% Show page(s) 1
%%
\documentclass[]{exaarticle}
\pagestyle{empty}
\setlength\textwidth{375.57637pt}
\AtBeginDocument{\setlength\parindent{0pt}}
\StartShownPreambleCommands
\usepackage{mathtools,esint} \newcommand*\diff{\mathop{}\!\mathrm{d}}
\StopShownPreambleCommands
\begin{document}
\begin{align*}
\iiint\limits_Rf(x,y,z)\diff R
&= \int\limits_{z_1}^{z_2}
\int\limits_{\varphi_1(z)}^{\varphi_2(z)}
\int\limits_{r_1(\varphi,z)}^{r_2(\varphi,z)}
F(r,\varphi,z)r\diff r\diff\varphi\diff z\\
%\ArrowBetweenLines[\Downarrow]% left hand side
\ArrowBetweenLines* % right hand side (\Updownarrow is the default)
&= \int\limits_{\varphi_1(z)}^{\varphi_2(z)}
\int\limits_{\vartheta_1(\varphi)}^{\vartheta_2(\varphi)}
\int\limits_{r_1(\vartheta,\varphi)}^{r_2(\vartheta,\varphi)}
F(r,\vartheta,\varphi)r^2\sin\vartheta\diff r\,r\diff\vartheta\diff\varphi
\end{align*}
\end{document}
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