\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} {\bf Grammar} Some of these iterated
integrals correspond to real geometric problems (computation of
volumes) and some do not. Some are actually illegal! Please indicate
which are good and which are not.  Explain your answers. Compute any
iterated integral which corresponds to a volume, and make a rough
sketch of each volume computed.

\medskip

\settabs 2 \columns
\+a) $\displaystyle{\int_{0}^{x^3}\int_{0}^{y}{x^2+y^2+ 1}\; dx\; dy}$ 
&b) $\displaystyle{\int_{0}^{1}\int_{0}^{5x}{x^2+y^2+ 1}\; dx\; dy}$\cr

\medskip
\+c) $\displaystyle{\int_{5}^{7}\int_{y^3}^{3y}{x^2+y^2+ 1}\; dx\; dy}$
&d) $\displaystyle{\int_{-1}^{0}\int_{2y}^{-y^2}{x^2+y^2+ 1}\; dx\; dy}$\cr


 









\vfil\eject\end