\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} The region $R$ is bounded below by the $x$-axis, bounded on
the left by the line $x=1$, bounded on the right by the line $x=2$,
and bounded above by the curve
$\displaystyle
y = {{5+x}\over{x^2+4x+3}}
$.

\medskip

\noindent a) Sketch the region $R$ and set up a definite integral that
gives the area of  $R$. Then calculate the integral in two ways:

\smallskip

\item{i)} \underbar{Approximately} using the {\tt fnInt( } program in
your calculator.

\smallskip

\item{ii)} \underbar{Exactly} using the method of partial fractions.

\smallskip

\item{iii)} \underbar{Check} that the two answers are ``the same'' (that is,
find approximate values for the result of the second method).

\medskip

\noindent b) The region $R$ is rotated around the $x$-axis to generate
a solid body $B$.  Sketch $B$ and set up a definite integral that
gives the volume of $B$. Calculate the integral in two ways:

\smallskip

\item{i)} \underbar{Approximately} using the {\tt fnInt( } program in
your calculator.

\smallskip

\item{ii)} \underbar{Exactly} using the method of partial fractions
(be careful how you set this up -- there are {\it four} undetermined
coefficients in the partial fraction decomposition).

\smallskip

\item{iii)} \underbar{Check} that the two answers are ``the same''
(that is, find approximate values for the result of the second
method).

\vfil\eject\end