\subsection{\bf How Do You Choose Correct Strategy?}

\begin{slide}

\begin{itemize}
\item d) General Advice

$\bullet$\ \ The user must ``stare'' at his or her
function and decide on ``correct'' choice of strategy.

$\bullet$\ \ There will be many correct choices.

$\bullet$\ \ One can mix strategies and also may need
different strategies in different regions.

$\bullet$\ \ Consider
$$
I = \int^\infty_0 {1\over\sqrt{x}} \left\lbrack \exp\left( -x^3
\right) + \exp (-x)\right\rbrack\,dx = I_1 + I_2
$$

\item with $I_1$ given by
$$
I_1 = \int^{x\sim 1}_0 {1\over\sqrt{x}} \left\lbrack \exp\left(
-x^3 \right) + \exp (-x)\right\rbrack\,dx.
$$

\item Use change of variables $y=2\sqrt{x}$ $\underline{\rm or}$
weight $w(x)=1/\sqrt{x}$ formula.
\end{itemize}
\end{slide}


