mailing-list for TeXmacs Users

[Friedrich Laher <address@hidden>]

pagebreaking of  1.99.4
makes me cry



<TeXmacs|1.99.4>

<style|<tuple|generic|german>>

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  <math|<frac|1|2*<sqrt|x>>*\<mathd\>x=\<mathd\>u>>>|<row|<cell|<math|\<mathd\>x=2*u*\<mathd\>u>>>|<row|<cell|<math|I<rsub|V>=<big|int><frac|u<rsup|3>|1+u<rsup|4>>\<cdot\>2*u*\<mathd\>u>>>|<row|<cell|<math|<with|math-display|true|I<rsub|V>=2*<big|int><frac|u<rsup|4>|1+u<rsup|4>>*\<mathd\>u>>>>|<row|<cell|<math|><math|<frac|u<rsup|4>|1+u<rsup|4>>=1-<frac|1|1+u<rsup|4>>>>>|<row|<cell|<math|I<rsub|V>=2*u-I>>>|<row|<cell|zu
  bestimmen ist also noch>>|<row|<cell|<with|math-display|true|<math|I=<big|int>><math|<frac|1|1+u<rsup|4>>**\<mathd\>u>>>>>>>>>>>>

  <\eqnarray*>
    <tformat|<table|<row|<cell|I>|<cell|=>|<cell|<big|int><frac|\<mathd\>u|<around*|(|1+u<rsup|2>|)><rsup|2>-2*u<rsup|2>>=<big|int><frac|\<mathd\>u|<around*|(|1+<sqrt|2>*u+u<rsup|2>|)><around*|(|1-<sqrt|2>*u+u<rsup|2>|)>>>>|<row|<cell|>|<cell|=>|<cell|<big|int><around*|(|<frac|a*u+b|1+<sqrt|2>*u+u<rsup|2>>+<frac|c*u+d|1-<sqrt|2>*u+u<rsup|2>>|)>*\<mathd\>u>>|<row|<cell|>|<cell|=>|<cell|<big|int><around*|(|<frac|u<rsup|0>*<around*|(|b+d|)>+u*<around*|(|a-b*<sqrt|2>+c+d*<sqrt|2>|)>+u<rsup|2>*<around*|(|-a*<sqrt|2>+b+c*<sqrt|2>+d|)>+u<rsup|3>*<around*|(|a+c|)>|<around*|(|1+<sqrt|2>*u+u<rsup|2>|)><around*|(|1-<sqrt|2>*u+u<rsup|2>|)>>|)>*\<mathd\>u>>>>
  </eqnarray*>

  <no-page-break*>

  Der <math|u<rsup|0>->Koeffitient muÿ <math|=1> sein, alle übrigen
  =0;<space|2em><math|w\<assign\><sqrt|2>>

  <\equation*>
    <matrix|<tformat|<table|<row|<cell|>|<cell|>|<cell|a>|<cell|b>|<cell|c>|<cell|d>|<cell|=>>|<row|<cell|z0>|<cell|>|<cell|0>|<cell|1>|<cell|0>|<cell|1>|<cell|1>>|<row|<cell|z1>|<cell|>|<cell|1>|<cell|-w>|<cell|1>|<cell|w>|<cell|0>>|<row|<cell|z2>|<cell|>|<cell|-w>|<cell|1>|<cell|w>|<cell|1>|<cell|0>>|<row|<cell|z3>|<cell|>|<cell|1>|<cell|0>|<cell|1>|<cell|0>|<cell|0>>>>><text|<space|1em>>z1\<leftrightarrows\>z0<text|<space|1em>>\<Rightarrow\><text|<space|1em>><matrix|<tformat|<table|<row|<cell|>|<cell|>|<cell|a>|<cell|b>|<cell|c>|<cell|d>|<cell|=>|<cell|>>|<row|<cell|z1>|<cell|>|<cell|1>|<cell|-w>|<cell|1>|<cell|w>|<cell|0>|<cell|>>|<row|<cell|z0>|<cell|>|<cell|0>|<cell|1>|<cell|0>|<cell|1>|<cell|1>|<cell|>>|<row|<cell|z2>|<cell|>|<cell|-w>|<cell|1>|<cell|w>|<cell|1>|<cell|0>|<cell|>>|<row|<cell|z3>|<cell|>|<cell|1>|<cell|0>|<cell|1>|<cell|0>|<cell|0>|<cell|>>>>>
  </equation*>

  <\equation*>
    <text|<space|1em>><tabular|<tformat|<cwith|1|-1|1|-1|cell-halign|c>|<cwith|3|3|1|-1|cell-tborder|0ln>|<cwith|2|2|1|-1|cell-bborder|0ln>|<cwith|3|3|1|-1|cell-bborder|1ln>|<cwith|4|4|1|-1|cell-tborder|1ln>|<cwith|3|3|1|1|cell-lborder|0ln>|<cwith|3|3|7|7|cell-rborder|0ln>|<cwith|4|4|1|3|cell-halign|c>|<cwith|5|5|1|-1|cell-tborder|0ln>|<cwith|4|4|1|-1|cell-bborder|0ln>|<cwith|5|5|1|-1|cell-bborder|1ln>|<cwith|5|5|1|1|cell-lborder|0ln>|<cwith|5|5|7|7|cell-rborder|0ln>|<cwith|2|2|3|7|cell-tborder|0ln>|<cwith|1|1|3|7|cell-bborder|0ln>|<cwith|2|2|3|7|cell-bborder|1ln>|<cwith|3|3|3|7|cell-tborder|1ln>|<cwith|2|2|3|3|cell-lborder|0ln>|<cwith|2|2|7|7|cell-rborder|0ln>|<table|<row|<cell|z2>|<cell|>|<cell|-w>|<cell|1>|<cell|w>|<cell|1>|<cell|0>>|<row|<cell|+w*z1>|<cell|>|<cell|+w>|<cell|-2>|<cell|w>|<cell|2>|<cell|0>>|<row|<cell|=>|<cell|>|<cell|0>|<cell|-1>|<cell|2*w>|<cell|3>|<cell|0>>|<row|<cell|z3>|<cell|>|<cell|1>|<cell|0>|<cell|1>|<cell|0>|<cell|0>>|<row|<cell|-z1>|<cell|>|<cell|-1>|<cell|w>|<cell|-1>|<cell|-w>|<cell|0>>|<row|<cell|=>|<cell|>|<cell|0>|<cell|w>|<cell|0>|<cell|-*w>|<cell|0>>>>><text|<space|1em>>\<Rightarrow\><text|
    ><matrix|<tformat|<cwith|4|4|3|7|cell-halign|c>|<cwith|5|5|3|7|cell-halign|c>|<cwith|4|4|3|7|cell-tborder|0ln>|<cwith|3|3|3|7|cell-bborder|0ln>|<cwith|4|4|3|7|cell-bborder|0ln>|<cwith|5|5|3|7|cell-tborder|0ln>|<cwith|4|4|3|3|cell-lborder|0ln>|<cwith|4|4|2|2|cell-rborder|0ln>|<cwith|4|4|7|7|cell-rborder|0ln>|<table|<row|<cell|>|<cell|>|<cell|a>|<cell|b>|<cell|c>|<cell|d>|<cell|=>>|<row|<cell|z1>|<cell|>|<cell|1>|<cell|-w>|<cell|1>|<cell|w>|<cell|0>>|<row|<cell|z0>|<cell|>|<cell|0>|<cell|1>|<cell|0>|<cell|1>|<cell|1>>|<row|<cell|z2>|<cell|>|<cell|0>|<cell|-1>|<cell|2*w>|<cell|3>|<cell|0>>|<row|<cell|z3>|<cell|>|<cell|0>|<cell|w>|<cell|0>|<cell|-*w>|<cell|0>>>>>
  </equation*>

  <\equation*>
    <text|<space|2em>><tabular*|<tformat|<cwith|1|1|3|7|cell-halign|c>|<cwith|1|1|3|7|cell-tborder|0ln>|<cwith|1|1|3|3|cell-tborder|0ln>|<cwith|1|1|3|3|cell-lborder|0ln>|<cwith|1|1|4|7|cell-tborder|0ln>|<cwith|1|1|4|4|cell-lborder|0ln>|<cwith|1|1|3|3|cell-rborder|0ln>|<cwith|1|1|7|7|cell-rborder|0ln>|<cwith|3|3|1|-1|cell-tborder|0ln>|<cwith|2|2|1|-1|cell-bborder|0ln>|<cwith|3|3|1|-1|cell-bborder|1ln>|<cwith|4|4|1|-1|cell-tborder|1ln>|<cwith|3|3|1|1|cell-lborder|0ln>|<cwith|3|3|7|7|cell-rborder|0ln>|<cwith|4|4|3|7|cell-halign|c>|<cwith|5|5|3|7|cell-halign|c>|<cwith|5|5|3|7|cell-tborder|0ln>|<cwith|5|5|3|7|cell-bborder|1ln>|<cwith|5|5|7|7|cell-rborder|0ln>|<cwith|2|2|3|7|cell-tborder|0ln>|<cwith|1|1|3|7|cell-bborder|0ln>|<cwith|2|2|3|7|cell-bborder|1ln>|<cwith|3|3|3|7|cell-tborder|1ln>|<cwith|2|2|7|7|cell-rborder|0ln>|<cwith|6|6|2|2|cell-rborder|0ln>|<cwith|6|6|2|2|cell-rborder|0ln>|<cwith|6|6|2|2|cell-rborder|0ln>|<cwith|2|2|1|2|cell-tborder|0ln>|<cwith|1|1|1|2|cell-bborder|0ln>|<cwith|2|2|1|2|cell-bborder|1ln>|<cwith|3|3|1|2|cell-tborder|1ln>|<cwith|2|2|1|1|cell-lborder|0ln>|<cwith|2|2|2|2|cell-rborder|0ln>|<cwith|2|2|3|3|cell-lborder|0ln>|<cwith|5|5|1|2|cell-tborder|0ln>|<cwith|4|4|1|2|cell-bborder|0ln>|<cwith|5|5|1|2|cell-bborder|1ln>|<cwith|6|6|1|2|cell-tborder|1ln>|<cwith|5|5|1|1|cell-lborder|0ln>|<cwith|5|5|2|2|cell-rborder|0ln>|<cwith|5|5|3|3|cell-lborder|0ln>|<table|<row|<cell|z2>|<cell|>|<cell|0>|<cell|-1>|<cell|2w>|<cell|3>|<cell|0>>|<row|<cell|+z0>|<cell|>|<cell|0>|<cell|1>|<cell|0>|<cell|1>|<cell|1>>|<row|<cell|=>|<cell|>|<cell|0>|<cell|0>|<cell|2**w>|<cell|4>|<cell|1>>|<row|<cell|z3>|<cell|>|<cell|0>|<cell|w>|<cell|0>|<cell|-*w>|<cell|0>>|<row|<cell|+w*z2>|<cell|>|<cell|0>|<cell|-w>|<cell|4>|<cell|3*w>|<cell|0>>|<row|<cell|=>|<cell|>|<cell|0>|<cell|0>|<cell|4>|<cell|2*w>|<cell|0>>>>><text|<space|1em>>\<Rightarrow\><text|
    ><matrix|<tformat|<cwith|4|4|3|7|cell-tborder|0ln>|<cwith|3|3|3|7|cell-bborder|0ln>|<cwith|4|4|3|7|cell-bborder|0ln>|<cwith|5|5|3|7|cell-tborder|0ln>|<cwith|4|4|3|3|cell-lborder|0ln>|<cwith|4|4|2|2|cell-rborder|0ln>|<cwith|4|4|7|7|cell-rborder|0ln>|<table|<row|<cell|>|<cell|>|<cell|a>|<cell|b>|<cell|c>|<cell|d>|<cell|=>>|<row|<cell|z1>|<cell|>|<cell|1>|<cell|-w>|<cell|1>|<cell|w>|<cell|0>>|<row|<cell|z0>|<cell|>|<cell|0>|<cell|1>|<cell|0>|<cell|1>|<cell|1>>|<row|<cell|z2>|<cell|>|<cell|0>|<cell|0>|<cell|2**w>|<cell|4>|<cell|1>>|<row|<cell|z3>|<cell|>|<cell|0>|<cell|0>|<cell|4>|<cell|2*w>|<cell|0>>>>>
  </equation*>

  <\equation*>
    <tabular*|<tformat|<cwith|1|1|3|7|cell-tborder|0ln>|<cwith|2|2|3|7|cell-tborder|0ln>|<cwith|1|1|3|7|cell-bborder|0ln>|<cwith|2|2|3|7|cell-bborder|1ln>|<cwith|3|3|3|7|cell-tborder|1ln>|<cwith|2|2|3|3|cell-lborder|0ln>|<cwith|2|2|2|2|cell-rborder|0ln>|<cwith|2|2|7|7|cell-rborder|0ln>|<table|<row|<cell|z3>|<cell|>|<cell|0>|<cell|0>|<cell|4>|<cell|2*w>|<cell|0>>|<row|<cell|-w*z2>|<cell|>|<cell|0>|<cell|0>|<cell|-4>|<cell|-4w>|<cell|-w>>|<row|<cell|=>|<cell|>|<cell|0>|<cell|0>|<cell|0>|<cell|-2*w>|<cell|-w>>>>><text|<space|2em>>\<Rightarrow\><text|<space|2em>>
    <matrix|<tformat|<cwith|4|4|3|7|cell-tborder|0ln>|<cwith|3|3|3|7|cell-bborder|0ln>|<cwith|4|4|3|7|cell-bborder|0ln>|<cwith|5|5|3|7|cell-tborder|0ln>|<cwith|4|4|3|3|cell-lborder|0ln>|<cwith|4|4|2|2|cell-rborder|0ln>|<cwith|4|4|7|7|cell-rborder|0ln>|<table|<row|<cell|>|<cell|>|<cell|a>|<cell|b>|<cell|c>|<cell|d>|<cell|=>>|<row|<cell|z1>|<cell|>|<cell|1>|<cell|-w>|<cell|1>|<cell|w>|<cell|0>>|<row|<cell|z0>|<cell|>|<cell|0>|<cell|1>|<cell|0>|<cell|1>|<cell|1>>|<row|<cell|z2>|<cell|>|<cell|0>|<cell|0>|<cell|2**w>|<cell|4>|<cell|1>>|<row|<cell|z3>|<cell|>|<cell|0>|<cell|0>|<cell|0>|<cell|-2*w>|<cell|-w>>>>>
  </equation*>

  \;

  <\equation*>
    h\<assign\><frac|1|2>;<text| ><tabular*|<tformat|<table|<row|<cell|<frac|z3|-2w>=>|<cell|0>|<cell|0>|<cell|0>|<cell|1>|<cell|h>>>>>\<Rightarrow\><matrix|<tformat|<cwith|4|4|3|7|cell-tborder|0ln>|<cwith|3|3|3|7|cell-bborder|0ln>|<cwith|4|4|3|7|cell-bborder|0ln>|<cwith|5|5|3|7|cell-tborder|0ln>|<cwith|4|4|3|3|cell-lborder|0ln>|<cwith|4|4|7|7|cell-rborder|0ln>|<table|<row|<cell|>|<cell|>|<cell|a>|<cell|b>|<cell|c>|<cell|d>|<cell|=>>|<row|<cell|z1>|<cell|>|<cell|1>|<cell|-w>|<cell|1>|<cell|w>|<cell|0>>|<row|<cell|z0>|<cell|>|<cell|0>|<cell|1>|<cell|0>|<cell|1>|<cell|1>>|<row|<cell|z2>|<cell|>|<cell|0>|<cell|0>|<cell|2**w>|<cell|4>|<cell|1>>|<row|<cell|z3>|<cell|>|<cell|0>|<cell|0>|<cell|0>|<cell|1>|<cell|h>>>>>
  </equation*>

  <\equation*>
    <tabular*|<tformat|<cwith|1|1|2|6|cell-tborder|0ln>|<cwith|1|1|2|2|cell-lborder|0ln>|<cwith|1|1|6|6|cell-rborder|0ln>|<cwith|2|2|1|-1|cell-tborder|0ln>|<cwith|1|1|1|-1|cell-bborder|0ln>|<cwith|2|2|1|1|cell-tborder|0ln>|<cwith|1|1|1|1|cell-bborder|0ln>|<cwith|2|2|1|1|cell-lborder|0ln>|<cwith|3|3|1|-1|cell-tborder|0ln>|<cwith|2|2|1|-1|cell-bborder|0ln>|<cwith|3|3|1|-1|cell-bborder|1ln>|<cwith|3|3|1|1|cell-lborder|0ln>|<cwith|3|3|6|6|cell-rborder|0ln>|<cwith|5|5|2|-1|cell-tborder|0ln>|<cwith|4|4|2|-1|cell-bborder|0ln>|<cwith|5|5|2|-1|cell-bborder|1ln>|<cwith|6|6|2|-1|cell-tborder|1ln>|<cwith|5|5|2|2|cell-lborder|0ln>|<cwith|5|5|1|1|cell-rborder|0ln>|<cwith|5|5|6|6|cell-rborder|0ln>|<cwith|2|2|2|-1|cell-tborder|0ln>|<cwith|1|1|2|-1|cell-bborder|0ln>|<cwith|2|2|2|-1|cell-bborder|1ln>|<cwith|3|3|2|-1|cell-tborder|1ln>|<cwith|2|2|2|2|cell-lborder|0ln>|<cwith|2|2|1|1|cell-rborder|0ln>|<cwith|2|2|6|6|cell-rborder|0ln>|<table|<row|<cell|z2>|<cell|0>|<cell|0>|<cell|2**w>|<cell|4>|<cell|1>>|<row|<cell|-4*z3>|<cell|0>|<cell|0>|<cell|0>|<cell|-4>|<cell|-2>>|<row|<cell|=>|<cell|0>|<cell|0>|<cell|2*w>|<cell|0>|<cell|-1>>|<row|<cell|z1>|<cell|1>|<cell|-w>|<cell|1>|<cell|w>|<cell|0>>|<row|<cell|-w*z3>|<cell|0>|<cell|0>|<cell|0>|<cell|-w>|<cell|-w*h>>|<row|<cell|=>|<cell|1>|<cell|-w>|<cell|1>|<cell|0>|<cell|-w*h>>>>><tabular*|<tformat|<table|<row|<cell|>|<cell|\<Rightarrow\>>|<cell|>>>>><matrix|<tformat|<cwith|3|4|3|3|cell-lborder|0ln>|<cwith|3|4|2|2|cell-rborder|0ln>|<cwith|3|4|7|7|cell-rborder|0ln>|<cwith|3|3|3|7|cell-bborder|0ln>|<cwith|3|3|3|3|cell-lborder|0ln>|<cwith|3|3|2|2|cell-rborder|0ln>|<cwith|3|3|7|7|cell-rborder|0ln>|<cwith|5|5|6|8|cell-tborder|0ln>|<cwith|5|5|6|8|cell-tborder|0ln>|<cwith|4|4|3|7|cell-tborder|0ln>|<cwith|4|4|7|7|cell-rborder|0ln>|<cwith|2|2|3|7|cell-tborder|0ln>|<cwith|1|1|3|7|cell-bborder|0ln>|<cwith|2|2|3|7|cell-bborder|0ln>|<cwith|3|3|3|7|cell-tborder|0ln>|<cwith|2|2|3|3|cell-lborder|0ln>|<cwith|2|2|2|2|cell-rborder|0ln>|<cwith|2|2|7|7|cell-rborder|0ln>|<cwith|5|5|3|7|cell-tborder|0ln>|<cwith|4|4|3|7|cell-bborder|0ln>|<cwith|5|5|3|7|cell-bborder|0ln>|<cwith|5|5|3|3|cell-lborder|0ln>|<cwith|5|5|2|2|cell-rborder|0ln>|<cwith|5|5|7|7|cell-rborder|0ln>|<table|<row|<cell|>|<cell|>|<cell|a>|<cell|b>|<cell|c>|<cell|d>|<cell|=>>|<row|<cell|z1>|<cell|>|<cell|1>|<cell|-w>|<cell|1>|<cell|0>|<cell|-w*h>>|<row|<cell|z0>|<cell|>|<cell|0>|<cell|1>|<cell|0>|<cell|0>|<cell|h>>|<row|<cell|z2>|<cell|>|<cell|0>|<cell|0>|<cell|2*w>|<cell|0>|<cell|-1>>|<row|<cell|z3>|<cell|>|<cell|0>|<cell|0>|<cell|0>|<cell|1>|<cell|h>>>>><tabular*|<tformat|<table|<row|<cell|>|<cell|z2\<assign\><frac|z2|2*w>>>>>><tabular*|<tformat|<table|<row|<cell|\<Rightarrow\>>|<cell|>>>>><matrix|<tformat|<cwith|3|4|3|3|cell-lborder|0ln>|<cwith|3|4|2|2|cell-rborder|0ln>|<cwith|3|4|7|7|cell-rborder|0ln>|<cwith|3|3|3|7|cell-bborder|0ln>|<cwith|3|3|3|3|cell-lborder|0ln>|<cwith|3|3|2|2|cell-rborder|0ln>|<cwith|3|3|7|7|cell-rborder|0ln>|<cwith|5|5|6|8|cell-tborder|0ln>|<cwith|5|5|6|8|cell-tborder|0ln>|<cwith|4|4|3|7|cell-tborder|0ln>|<cwith|4|4|7|7|cell-rborder|0ln>|<cwith|2|2|3|7|cell-tborder|0ln>|<cwith|1|1|3|7|cell-bborder|0ln>|<cwith|2|2|3|7|cell-bborder|0ln>|<cwith|3|3|3|7|cell-tborder|0ln>|<cwith|2|2|3|3|cell-lborder|0ln>|<cwith|2|2|2|2|cell-rborder|0ln>|<cwith|2|2|7|7|cell-rborder|0ln>|<cwith|5|5|3|7|cell-tborder|0ln>|<cwith|4|4|3|7|cell-bborder|0ln>|<cwith|5|5|3|7|cell-bborder|0ln>|<cwith|5|5|3|3|cell-lborder|0ln>|<cwith|5|5|2|2|cell-rborder|0ln>|<cwith|5|5|7|7|cell-rborder|0ln>|<table|<row|<cell|>|<cell|>|<cell|a>|<cell|b>|<cell|c>|<cell|d>|<cell|=>>|<row|<cell|z1>|<cell|>|<cell|1>|<cell|-w>|<cell|1>|<cell|0>|<cell|-w*h>>|<row|<cell|z0>|<cell|>|<cell|0>|<cell|1>|<cell|0>|<cell|0>|<cell|h>>|<row|<cell|z2>|<cell|>|<cell|0>|<cell|0>|<cell|1>|<cell|0>|<cell|-h/w>>|<row|<cell|z3>|<cell|>|<cell|0>|<cell|0>|<cell|0>|<cell|1>|<cell|h>>>>>
  </equation*>

  <\equation*>
    <tabular*|<tformat|<cwith|1|1|2|6|cell-tborder|0ln>|<cwith|1|1|2|6|cell-bborder|0ln>|<cwith|1|1|2|2|cell-lborder|0ln>|<cwith|1|1|6|6|cell-rborder|0ln>|<cwith|3|3|2|-1|cell-tborder|0ln>|<cwith|2|2|2|-1|cell-bborder|0ln>|<cwith|3|3|2|-1|cell-bborder|1ln>|<cwith|4|4|2|-1|cell-tborder|1ln>|<cwith|3|3|2|2|cell-lborder|0ln>|<cwith|3|3|1|1|cell-rborder|0ln>|<cwith|3|3|6|6|cell-rborder|0ln>|<table|<row|<cell|z1>|<cell|1>|<cell|-w>|<cell|1>|<cell|0>|<cell|-w*h>>|<row|<cell|+w*z0>|<cell|>|<cell|+w>|<cell|>|<cell|>|<cell|+w*h>>|<row|<cell|-z2>|<cell|0>|<cell|0>|<cell|-1>|<cell|0>|<cell|+h/w>>|<row|<cell|=>|<cell|1>|<cell|0>|<cell|0>|<cell|0>|<cell|+h/w>>>>><tabular*|<tformat|<table|<row|<cell|\<Rightarrow\>>|<cell|>>>>><matrix|<tformat|<cwith|3|4|2|2|cell-rborder|0ln>|<cwith|3|3|2|2|cell-rborder|0ln>|<cwith|5|5|6|8|cell-tborder|0ln>|<cwith|5|5|6|8|cell-tborder|0ln>|<cwith|2|2|2|2|cell-rborder|0ln>|<cwith|5|5|2|2|cell-rborder|0ln>|<cwith|4|4|2|2|cell-rborder|0ln>|<cwith|3|4|3|3|cell-lborder|0ln>|<cwith|3|4|7|7|cell-rborder|0ln>|<cwith|3|3|3|7|cell-bborder|0ln>|<cwith|3|3|3|3|cell-lborder|0ln>|<cwith|3|3|7|7|cell-rborder|0ln>|<cwith|5|5|6|7|cell-tborder|0ln>|<cwith|5|5|6|7|cell-tborder|0ln>|<cwith|3|3|3|7|cell-tborder|0ln>|<cwith|5|5|3|7|cell-tborder|0ln>|<cwith|5|5|3|7|cell-bborder|0ln>|<cwith|5|5|3|3|cell-lborder|0ln>|<cwith|5|5|7|7|cell-rborder|0ln>|<cwith|1|1|3|7|cell-tborder|0ln>|<cwith|1|1|3|7|cell-bborder|0ln>|<cwith|2|2|3|7|cell-tborder|0ln>|<cwith|1|1|3|3|cell-lborder|0ln>|<cwith|1|1|2|2|cell-rborder|0ln>|<cwith|1|1|7|7|cell-rborder|0ln>|<cwith|4|4|3|3|cell-lborder|0ln>|<cwith|4|4|7|7|cell-rborder|0ln>|<cwith|4|4|3|7|cell-tborder|0ln>|<cwith|4|4|7|7|cell-rborder|0ln>|<cwith|4|4|3|7|cell-bborder|0ln>|<table|<row|<cell|>|<cell|>|<cell|a>|<cell|b>|<cell|c>|<cell|d>|<cell|=>>|<row|<cell|z1>|<cell|>|<cell|1>|<cell|0>|<cell|0>|<cell|0>|<cell|+h/w>>|<row|<cell|z0>|<cell|>|<cell|0>|<cell|1>|<cell|0>|<cell|0>|<cell|h>>|<row|<cell|z2>|<cell|>|<cell|0>|<cell|0>|<cell|1>|<cell|0>|<cell|-h/w>>|<row|<cell|z3>|<cell|>|<cell|0>|<cell|0>|<cell|0>|<cell|1>|<cell|h>>>>>
  </equation*>

  <\equation*>
    h/w=<frac|1|2*<sqrt|2>>=<frac|<sqrt|2>|4><text| ;
    ><tabular*|<tformat|<cwith|1|-1|1|1|cell-lborder|1ln>|<cwith|1|-1|1|1|cell-rborder|0ln>|<cwith|1|-1|2|2|cell-lborder|0ln>|<cwith|1|1|1|1|cell-tborder|1ln>|<cwith|1|1|1|1|cell-lborder|1ln>|<cwith|2|2|1|1|cell-tborder|0ln>|<cwith|1|1|1|1|cell-bborder|0ln>|<cwith|2|2|1|1|cell-bborder|1ln>|<cwith|2|2|1|1|cell-lborder|1ln>|<cwith|1|1|2|5|cell-tborder|1ln>|<cwith|1|1|2|5|cell-bborder|0ln>|<cwith|2|2|2|5|cell-tborder|0ln>|<cwith|1|1|2|2|cell-lborder|0ln>|<cwith|1|1|1|1|cell-rborder|0ln>|<cwith|1|1|5|5|cell-rborder|0ln>|<cwith|1|1|6|6|cell-lborder|0ln>|<cwith|2|2|2|4|cell-tborder|0ln>|<cwith|1|1|2|4|cell-bborder|0ln>|<cwith|2|2|2|4|cell-bborder|1ln>|<cwith|2|2|2|2|cell-lborder|0ln>|<cwith|2|2|1|1|cell-rborder|0ln>|<cwith|2|2|5|5|cell-rborder|0ln>|<cwith|2|2|6|6|cell-lborder|0ln>|<cwith|1|1|5|6|cell-tborder|1ln>|<cwith|1|1|5|5|cell-lborder|0ln>|<cwith|1|1|4|4|cell-rborder|0ln>|<cwith|1|1|6|6|cell-rborder|1ln>|<cwith|2|2|5|6|cell-tborder|0ln>|<cwith|1|1|5|6|cell-bborder|0ln>|<cwith|2|2|5|6|cell-bborder|1ln>|<cwith|2|2|5|5|cell-lborder|0ln>|<cwith|2|2|4|4|cell-rborder|0ln>|<cwith|2|2|6|6|cell-rborder|1ln>|<table|<row|<cell|a>|<cell|=>|<cell|<frac|<sqrt|2>|4>>|<cell|b>|<cell|=>|<cell|<frac|1|2>>>|<row|<cell|c>|<cell|=>|<cell|<frac|-<sqrt|2>|4>>|<cell|d>|<cell|=>|<cell|<frac|1|2>>>>>>
  </equation*>

  <\eqnarray*>
    <tformat|<table|<row|<cell|\<Rightarrow\>I<big|int><around*|(|<frac|a*u+b|1+<sqrt|2>*u+u<rsup|2>>+<frac|c*u+d|1-<sqrt|2>*u+u<rsup|2>>|)>*\<mathd\>u>|<cell|=>|<cell|<frac|1|4>*<big|int><around*|(|<frac|<sqrt|2>u+2|1+<sqrt|2>*u+u<rsup|2>>+<frac|-<sqrt|2>*u+2|1-<sqrt|2>*u+u<rsup|2>>|)>*\<mathd\>u>>|<row|<cell|=<space|0.6spc><frac|1|4*<sqrt|2>>*<big|int><around*|(|<frac|2*u+2*<sqrt|2>|1+<sqrt|2>*u+u<rsup|2>>+<frac|-2**u+2*<sqrt|2>|1-<sqrt|2>*u+u<rsup|2>>|)>*\<mathd\>u>|<cell|=>|<cell|<frac|1|4*<sqrt|2>>*<big|int><around*|(|<frac|2*u+<sqrt|2>|1+<sqrt|2>*u+u<rsup|2>>-<frac|2**u-*<sqrt|2>|1-<sqrt|2>*u+u<rsup|2>>+K|)>*\<mathd\>u2*\<pi\>>>|<row|<cell|I>|<cell|=>|<cell|<frac|1|4*<sqrt|2>><around*|(|*ln<frac|1+<sqrt|2>*u+u<rsup|2>|1-<sqrt|2>*u+u<rsup|2>>+<big|int>K**\<mathd\>u|)>>>|<row|<cell|<text|mit<space|1em><math|<big|int>K**\<mathd\>u>>>|<cell|=>|<cell|<sqrt|2>*<big|int><around*|(|<frac|1|1+<sqrt|2>*u+u<rsup|2>>+<frac|1|1-<sqrt|2>*u+u<rsup|2>>|)>*\<mathd\>u>>|<row|<cell|<big|int>K**\<mathd\>u>|<cell|=>|<cell|<sqrt|2>*<big|int><around*|(|<frac|1|<around*|(|u+<sqrt|2>/2|)><rsup|2>+1/2>+<frac|1|<around*|(|u-<sqrt|2>/2|)><rsup|2>+1/2>|)>*\<mathd\>u>>|<row|<cell|<big|int>K**\<mathd\>u>|<cell|=>|<cell|2*<sqrt|2>*<big|int><around*|(|<frac|1|2<around*|(|u+<sqrt|2>/2|)><rsup|2>+1>+<frac|1|2<around*|(|u-<sqrt|2>/2|)><rsup|2>+1>|)>*\<mathd\>u>>|<row|<cell|>|<cell|=>|<cell|2*<sqrt|2>*<big|int><around*|(|<frac|1|<around*|(|<sqrt|2>*u+1|)><rsup|2>+1>+<frac|1|<around*|(|<sqrt|2>*u-1|)><rsup|2>+1>|)>*\<mathd\>u2*\<pi\>>>|<row|<cell|>|<cell|=>|<cell|<frac|2*<sqrt|2>|<sqrt|2>>*<around*|(|arctan<around*|(|<sqrt|2>*u+1|)>+arctan<around*|(|<sqrt|2>*u-1|)>|)>>>|<row|<cell|I>|<cell|=>|<cell|<frac|1|4*<sqrt|2>><around*|(|*ln<frac|1+<sqrt|2>*u+u<rsup|2>|1-<sqrt|2>*u+u<rsup|2>>+2*<around*|(|arctan<around*|(|<sqrt|2>*u+1|)>+arctan<around*|(|<sqrt|2>*u-1|)>|)>|)>>>|<row|<cell|<text|Rücksubstitution
    >u>|<cell|=>|<cell|<sqrt|x>>>|<row|<cell|I>|<cell|=>|<cell|<frac|1|4*<sqrt|2>><around*|(|*ln<frac|1+<sqrt|2*x>*+x|1-<sqrt|2*x>*+x>+2*<around*|(|arctan<around*|(|<sqrt|2*x>*+1|)>+arctan<around*|(|<sqrt|2*x>-1|)>|)>|)>>>|<row|<cell|<text|somit<space|1em>>V>|<cell|=>|<cell|2*\<pi\><above|<below|<big|int>|R<rsub|I>>|R<rsub|O>>x\<cdot\>f<around*|(|x|)>*\<cdot\><space|0.2spc>\<mathd\>x<space|0.2spc>>>|<row|<cell|>|<cell|=>|<cell|2*\<pi\><around*|\||2*<sqrt|x>-<frac|1|4*<sqrt|2>><around*|(|*ln<frac|1+<sqrt|2*x>*+x|1-<sqrt|2*x>*+x>+2*<around*|(|arctan<around*|(|<sqrt|2*x>*+1|)>+arctan<around*|(|<sqrt|2*x>-1|)>|)>|)>|\|><rsup|R<rsub|O>><rsub|R<rsub|I>>>>>>
  </eqnarray*>

  \V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\V\U

  Verfaÿt

  mit texmacs ( http://www.texmacs.org ),

  und Bild am Beginn mit geogebra ( http://www.geogebra.org ).

  Bild endet am rechten Rand der Kurve und unter dem <math|R<rsub|I><text|
  der Formel \ <math|<with|math-display|true|V=2\<cdot\>\<pi\><above|<below|<big|int>|R<rsub|I>>|R<rsub|O>>x\<cdot\>f<around*|(|x|)>*\<cdot\><space|0.2spc>\<mathd\>x>>
  ,>>

  Formel im Bild sind geogebra-gerendertes handcodiertes Latex

  <\equation*>
    <tabular*|<tformat|<table|<row|<cell|>>>>>
  </equation*>
</body>

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  <\collection>
    <associate|auto-1|<tuple|1|?>>
  </collection>
</references>

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