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%%
%% An UIT Edition example
%%
%% Example 09-17-6 on page 188.
%%
%% 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}
\newcommand*\diff{\mathop{}\!\mathrm{d}}
\StopShownPreambleCommands
\begin{document}
\[ s =
\begin{dcases}
\int\limits_a^b\sqrt{1+y\prime^2}\diff x & y=f(x)\\
\int\limits_{t_1}^{t_2}\sqrt{\dot{x}^2+\dot{y}^2}\diff t & x=f(t); y=f(t) \\
\int\limits_{\varphi_1}^{\varphi_2}
\sqrt{\left(\frac{\diff r}{\diff\varphi}\right)^2+r^2}\,\diff\varphi
& r=f(\varphi)
\end{dcases}
\]
\end{document}
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