\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Suppose that $a$ is a positive
constant and that $R$ is the region bounded above by $y = 1/{x^a}$,
below by $y = 0$, and on the left by the line $x = 1\thinspace $.

\medskip

\noindent a) Sketch the curves $y=1/x^a$ for $a=.5$, $1$ and
$2$. Which of these is closest to the $x$-axis?

\medskip

\noindent b) For which positive numbers $a$ do you get a convergent
integral when you attempt to calculate the area of $R$?

\medskip

\noindent c) Same as b), but for the volume of the solid obtained by
rotating $R$ around the $x$-axis.

\medskip

\noindent d) Same as c), but for the volume of the solid obtained by
rotating $R$ around the $y$-axis.

\vfil\eject\end