summaryrefslogtreecommitdiff
path: root/info/examples/Math/10-05-2.ltx
blob: e30977669e1cb436ea475e292a6e4e53565ec61b (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
%% 
%%  Ein Beispiel der DANTE-Edition
%%  Mathematiksatz mit LaTeX
%%  2. Auflage
%% 
%%  Beispiel 10-05-2 auf Seite 222.
%% 
%%  Copyright (C) 2012 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{352.81416pt}
\AtBeginDocument{\setlength\parindent{0pt}}
\StartShownPreambleCommands
\usepackage{amsmath,esint} \newcommand*\diff{\mathop{}\!\mathrm{d}}
\StopShownPreambleCommands
\begin{document}
\begin{align*}
\biggl(\int_{-\infty}^\infty e^{-x^2}\,dx\biggr)^2
  &= \int_{-\infty}^\infty\int_{-\infty}^\infty e^{-(x^2+y^2)}\diff x\diff y \\
  &= \int_0^{2\pi}\int_0^\infty e^{-r^2}r\diff r\diff\theta                  \\
  &= \int_0^{2\pi}\biggl(-{e^{-r^2}\over2}
        \bigg\vert_{r=0}^{r=\infty}\,\biggr)\diff\theta\\
  &= \pi                                                         \tag*{q.e.d.}
\end{align*}
\end{document}