\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Calculate four of the following integrals:
$$
\int x \cos x^2 \, dx\thinspace ;\ \
\int x^2 \cos x^2 \, dx\thinspace ;\ \
\int x^2 \cos x \, dx\thinspace ;\ \
\int x^2  \cos^2 x \, dx\thinspace ;\ \ 
\int x \cos^2 x \,dx\thinspace .
$$

\medskip

\noindent {\bf Comment} Most people use {\it many}\/ parentheses and
rewrite the integrands to decrease possible confusion. So
\underbar{$x^2 \cos^2 x$} becomes $\underline{x^2 (\cos x)^2}$ and
\underbar{$x^2 \cos x^2$} becomes $\underline{x^2\cos(x^2)}$.







\vfil\eject\end