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%%  Ein Beispiel der DANTE-Edition
%%  Mathematiksatz mit LaTeX
%%  3. Auflage
%%  Beispiel 06-03-16 auf Seite 102.
%%  Copyright (C) 2018 Herbert Voss
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%%  of the LaTeX Project Public License, either version 1.3
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\newcommand*\diff{\mathop{}\!\mathrm{d}}
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\begin{document}
\begin{equation}
\begin{array}{rl}
A_1
 &=\left|\int_0^1(f(x)-g(x))\diff x\right|+\left|\int_1^2(g(x)-h(x))\diff x\right|\\
 &=\left|\int_0^1(x^2-3x)\diff x\right|+\left|\int_1^2(x^2-5x+6)\diff x\right|\\
 &=\left|\frac{x^3}{3}-\frac{3}{2}x^2\right|_0^1+\left|\frac{x^3}{3}
     -\frac{5}{2}x^2+6x\right|_1^2\\
 &=\left|\frac13-\frac32\right|+\left|\frac83-\frac{20}{2}+12-\left(\frac13
     -\frac{5}{2}+6\right)\right|\\
 &=\left|-\frac76\right|+\left|\frac{28}{6}-\frac{23}{6}\right|=\frac76
     +\frac{5}{6}=2\,\textrm{FE}
\end{array}
\end{equation}
\end{document}