
\subsection{\bf Use of Bounding Boxes}
\subsection{\bf to Calculate $\pi$ --- I}

\begin{slide}
\begin{itemize}

\item (ii) Complicated Domains

\item One advantage of the Monte Carlo method is that it can
very easily take account of complicated integration domains.

\item We illustrate this first with a simple example---calculation of
$\pi$.

\centerline{\psfig{figure=ni.fig9.ps,clip=true,width=2.0in}}

\item Suppose we wished to calculate the integral over the inside
of the circle
$$
I = \int_{x^2 = y^2 \le 1} \, g(x,y)\,dx\,dy.
$$
\item One way of doing this is to put
$$\vbox{\halign{#\hfil\tabskip=2em&#\hfil&#\hfil\tabskip=0pt\cr
$g'(x,y)$ & $ = g(x,y)$ & $x^2 + y^2 \le 1$\cr
& = 0 & $x^2 + y^2 > 1$\cr
}}$$
\end{itemize}
\end{slide}


