%% LyX 1.1 created this file.  For more info, see http://www.lyx.org/.
%% Do not edit unless you really know what you are doing.
\documentclass[11pt,oneside]{amsart}
\usepackage[T1]{fontenc}
\usepackage{geometry}
\geometry{verbose,letterpaper,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in}
\setlength\parskip{\medskipamount}
\setlength\parindent{0pt}

\makeatletter


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% LyX specific LaTeX commands.
\providecommand{\LyX}{L\kern-.1667em\lower.25em\hbox{Y}\kern-.125emX\@}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Textclass specific LaTeX commands.
 \theoremstyle{plain}    
 \newtheorem{thm}{Theorem}[section]
 \numberwithin{equation}{section} %% Comment out for sequentially-numbered
 \numberwithin{figure}{section} %% Comment out for sequentially-numbered
 \theoremstyle{definition}
  \newtheorem{example}[thm]{Example}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands.
\setcounter{section}{5}
\setcounter{subsection}{1}

\makeatother

\begin{document}


\title{On-line Math 21}


\email{david.johnson@lehigh.edu}


\urladdr{http://www.lehigh.edu/\textasciitilde{}dlj0}

\maketitle

\subsection{The Fundamental Theorem of Calculus}

\textit{.} 

\begin{example}
\[
\int _{-1}^{2}|x|dx.\]
 
\end{example}

\subsubsection*{Solution }

Here you have to split it up into two pieces: \[
\int _{-1}^{2}|x|dx=\int _{-1}^{0}|x|dx+\int _{0}^{2}|x|dx.\]
 The first integral has \( x \) always negative, and the second has \( x \)
always positive, so we can remove the absolute value signs:\textit{\begin{eqnarray*}
\int _{-1}^{2}|x|dx & = & \int _{-1}^{0}|x|dx+\int _{0}^{2}|x|dx\\
 & = & \int _{-1}^{0}-xdx+\int _{0}^{2}xdx\\
 & = & \left. -x^{2}/2\right| _{-1}^{0}+\left. x^{2}/2\right| _{0}^{2}\\
 & = & (0-(-1/2))+(4/2-0)=5/2.
\end{eqnarray*}
}

The only {}``antidifferentiation{}'' trick we use here is that \[
\left( \frac{1}{2}x^{2}\right) '=x,\]
which certainly is true.
\end{document}
