\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Suppose that
$f(x,y)=(y-x^2)e^{x^2+y^2}$. Determine which of the integrals $I_1$,
$I_2$, $I_3$, and $I_4$ below is largest, which next largest,
etc. Explain carefully how you reached your conclusions. Do not
attempt to evaluate the integrals explicitly.
 
$$\matrix{\displaystyle I_1=\int_0^2\int_0^4 f(x,y)\,dy\,dx\ \
& \displaystyle I_2=\int_0^2\int_0^{x^2} f(x,y)\,dy\,dx\cr
\noalign{\smallskip}
\displaystyle I_3=\int_0^2\int_{x^2}^4 f(x,y)\,dy\,dx\ \
& \displaystyle I_4=\int_0^2\int_0^4 |f(x,y)|\,dy\,dx\cr}
$$

\noindent {\bf Hint} Where is $f$ positive? Where negative?  

\vfil\eject\end