%% This document created by Scientific Notebook (R) Version 3.0


\documentclass[12pt,thmsa]{article}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{sw20jart}

%TCIDATA{TCIstyle=article/art4.lat,jart,sw20jart}

%TCIDATA{<META NAME="ViewSettings" CONTENT="23">}
%TCIDATA{<META NAME="GraphicsSave" CONTENT="32">}
%TCIDATA{<META NAME="Title" CONTENT="Reference/Mathematics/Surface Area">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Sun Mar 30 14:10:11 1997}
%TCIDATA{Language=American English}
%TCIDATA{CSTFile=Reference.cst}
%TCIDATA{PageSetup=72,72,72,72,0}
%TCIDATA{<LINK REL="contents" HREF="..\Reference\ReferenceIndex.tex#Reference Index">}
%TCIDATA{<LINK REL="next" HREF="cal12_07.tex">}
%TCIDATA{<LINK REL="parent" HREF="CAL_contents.tex">}
%TCIDATA{<LINK REL="previous" HREF="cal12_05.tex">}
%TCIDATA{AllPages=
%F=36,\PARA{038<p type="texpara" tag="Body Text" >\hfill \thepage}
%}


\input{tcilatex}
\begin{document}


\section{Surface Area\label{Surface Area}}

\begin{definition}
Let $S$ be a surface with equation $z=f(x,y),$ where $f$ has continuous
partial derivatives. Assume that $f(x,y)\geq 0$ and the domain $D$ of $f$ is
a rectangle. then the \textbf{surface area} of $S$ is defined as 
\[
A(S)=\lim_{\left\| p\right\| \rightarrow
0}\sum_{i=1}^{m}\sum_{j=1}^{n}\Delta T_{ij}
\]
\end{definition}

\begin{definition}
The area of the surface with equation $z=f(x,y),(x,y)\in D$, where $f_{x}$
and $f_{y}$ are continuous, is 
\[
A(S)=\iint_{D}\sqrt{\left[ f_{x}(x,y)\right] ^{2}+\left[ f_{y}(x,y)\right]
^{2}+1}dA
\]
\end{definition}

\subsection{Related Scientific Notebook Topics}

\vspace{1pt}{\small \hyperref{Iterated integrals}{}{}{%
../../Help/DM7-8.tex#Iterated integrals}}

{\small \hyperref{Order of integration}{}{}{../../Help/DM7-8.tex#Order of
integration}}

\noindent \hrulefill

\begin{center}
\begin{tabular}{ccc}
{\small \hyperref{\FRAME{itbpF}{13.9375pt}{14.4375pt}{3pt}{}{}{nblogo.wmf}{%
\special{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 13.9375pt;height 14.4375pt;depth
3pt;original-width 24.0625pt;original-height 24.8125pt;cropleft "0";croptop
"0.9959";cropright "0.9937";cropbottom "0";filename
'Nblogo.wmf';file-properties "XNPEU";}}Computing Techniques}{}{}{%
../../Help/DMindex.tex}} & {\small \hyperref{\FRAME{itbpF}{13.9375pt}{%
14.4375pt}{3pt}{}{}{nblogo.wmf}{\special{language "Scientific Word";type
"GRAPHIC";maintain-aspect-ratio TRUE;display "PICT";valid_file "F";width
13.9375pt;height 14.4375pt;depth 3pt;original-width
24.0625pt;original-height 24.8125pt;cropleft "0";croptop "0.9959";cropright
"0.9937";cropbottom "0";filename 'Nblogo.wmf';file-properties "XNPEU";}}%
General Information}{}{}{../../Help/Index.tex}} & {\small \hyperref{\FRAME{%
itbpF}{13.9375pt}{14.4375pt}{3pt}{}{}{nblogo.wmf}{\special{language
"Scientific Word";type "GRAPHIC";maintain-aspect-ratio TRUE;display
"PICT";valid_file "F";width 13.9375pt;height 14.4375pt;depth
3pt;original-width 24.0625pt;original-height 24.8125pt;cropleft "0";croptop
"0.9959";cropright "0.9937";cropbottom "0";filename
'Nblogo.wmf';file-properties "XNPEU";}}Reference Library}{}{}{%
../ReferenceIndex.tex}}
\end{tabular}
\end{center}

\noindent \hrulefill

\end{document}
