\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} The curve $y=e^{-x}$, $x\ge0$, is
revolved about the $x$-axis. Does the resulting surface have finite or
infinite area?  (Remember that you can sometimes decide whether an
improper integral converges without calculating it exactly.)


%Exact answer: $2\pi\left( {1\over{\sqrt{2}}}+{1\over 2}{\rm arctanh} \left({1\over{\sqrt{2}}}\right)\right)\approx 7.21180$

\vfil\eject\end