(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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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[ 1804733, 52738]*) (*NotebookOutlinePosition[ 1805635, 52767]*) (* CellTagsIndexPosition[ 1805591, 52763]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Introduction to the Fundamental Theorem", "Title"], Cell["By Robin Sue Sanders, (Spring 1999)", "Subsubtitle", TextAlignment->Center], Cell["\<\ Credit for the initialization cells belongs to Ed Packel and Stan \ Wagon\ \>", "Subsubtitle"], Cell[CellGroupData[{ Cell[TextData[ "Definition of integral in terms of area\[LongDash]Review"], "Section"], Cell[TextData[{ "Recall that", StyleBox[" ", FontSize->17], Cell[BoxData[ \(TraditionalForm\`\[Integral]\_a\^b f[x]\ dx\)], FontSize->16], " gives the area under the curve ", Cell[BoxData[ FormBox[ StyleBox[\(y = f\ [x]\), FontSize->15], TraditionalForm]]], ", over the x-axis, and between the lines ", Cell[BoxData[ \(TraditionalForm\`x = a\)]], " and ", Cell[BoxData[ \(TraditionalForm\`x = b\)]], ". 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So the name of the variable of \ integration (the variable in the \"dx\" or \"dt\" part of the notation) is \ not important. We call it a ", StyleBox["dummy variable.", FontSlant->"Italic"], " (This is similar to why the counter in \[CapitalSigma] notation is \ called a dummy variable.) 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