\subsection{\bf Cunning Choice of Weight Functions}

\begin{slide}
\begin{itemize}

\item {\bf Strategy~II} is used when difficult function is
multiplicative, not additive.

\item Suppose

\begin{eqnarray*}
I&=&\int f(x) dx\ \ \ \ \ \mbox{where} \\
f(x)&=&f_1 (x)\, f_2 (x)\ \ \ \mbox{so that} \\
I&=&\int w(x)\, f_2 (x) \\
\mbox{with}&f_1 (x)& \mbox{viewed as a weight function}\ w(x). \\
\end{eqnarray*}

\item Use $f_1 (x)$ as a prescribed weight function to derive
special integration formulae for doing $\int w(x)$ polynomials.  We
described these earlier.  

\item This strategy applies to the case $f(x) =
{1\over\sqrt{x}}\exp\left( -x^3\right)$ with $w(x) = 1/\sqrt{x}$.
\end{itemize}
\end{slide}

