%% 
%%  Der Mathematiksatz mit LaTeX, 1. Auflage 2009
%% 
%%  Example 9-17-6 on page 199.
%% 
%%  Copyright (C) 2009 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.
%% 

\documentclass[]{ttctminimal}
\pagestyle{empty}
\setcounter{page}{6}
\setlength\textwidth{355.65944pt}
\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}