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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 292181, 11209]*) (*NotebookOutlinePosition[ 292836, 11232]*) (* CellTagsIndexPosition[ 292792, 11228]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ "How to prove in ", StyleBox["Mathematica", FontSlant->"Italic"], " " }], "Subtitle"], Cell["Exploot project", "Subsubtitle"], Cell["\<\ Ivan Cnop Vrije universiteit Brussel icnop@vub.ac.be\ \>", "Subsubtitle"], Cell[CellGroupData[{ Cell["The fundamental theorem of calculus", "Section"], Cell[CellGroupData[{ Cell["The statement", "Subsection"], Cell[BoxData[ \(\(Clear[f];\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(D[Integrate[f[t], {t, a, x}], x]\)], "Input"], Cell[BoxData[ \(f[x]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ FormBox[ FractionBox[\(\[PartialD]\((\[Integral]\_a\%x\( f( t)\) \[DifferentialD]t)\)\), \(\[PartialD]x\), MultilineFunction->None], TraditionalForm]], "Input"], Cell[BoxData[ \(f[x]\)], "Output"] }, Open ]], Cell[TextData[{ "Mathematica knows this theorem. \nThe condition that f should be ", StyleBox["continuous", FontWeight->"Bold"], " has to be checked each time we input a particular f . 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