%% 
%%  Ein Beispiel der DANTE-Edition
%%  Mathematiksatz mit LaTeX
%%  3. Auflage
%%  Beispiel 09-19-6 auf Seite 195.
%%  Copyright (C) 2018 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.
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\documentclass[10pt]{screxa}
\pagestyle{empty}
\setlength\textwidth{170.40707pt}
\AtBeginDocument{\setlength\parindent{0pt}}
%StartShownPreambleCommands
\usepackage{mathtools}
\newcommand*\diff{\mathop{}\!\mathrm{d}}
%StopShownPreambleCommands
\begin{document}
\[ s = \begin{dcases}
  \quad\int\limits_a^b\sqrt{1+y\prime^2}\diff x
     &  y=f(x)\\
  \quad\int\limits_{t_1}^{t_2}\sqrt{\dot{x}^2+
    \dot{y}^2}\diff t & x=f(t); y=f(t) \\
  \quad\int\limits_{\varphi_1}^{\varphi_2}
     \sqrt{\left(\frac{\diff r}{\diff\varphi}
  \right)^2+r^2}\,\diff\varphi & r=f(\varphi)
\end{dcases} \]
\end{document}