\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} The only information known
about a function $T$ and its derivatives is contained in this table: 

\medskip

\hskip 2.5in \vbox{
\def\tablerule{\noalign{\hrule depth0pt height.5pt width1.7in}}
\halign to \hsize{ \hfil $ # $\strut\quad \vrule\thinspace
& \hfil $ #
$\quad \vrule\thinspace &
\hfil $ # $\quad \vrule\thinspace
& \hfil $ # $\cr
\ x \negthinspace\hfil &\  T(x)
\negthinspace\negthinspace\negthinspace\hfil  &\
T'(x)\negthinspace\negthinspace\negthinspace\negthinspace  \hfil &\
T''(x)\negthinspace\negthinspace\negthinspace\negthinspace  \hfil\cr
\tablerule
\tablerule
1 & 2 & -2 & 2 \cr
\tablerule
2 & 3 & 6 & 5 \cr
\tablerule
3 & 7 & 4 & -4\cr
\tablerule
4 & 2 & 5 & 7 \cr}}
 
\vskip -.8in

\noindent a) Compute ${\int_2^3 T'(x)\, dx}$.

\medskip

\noindent b) Compute ${\int_2^3 T''(x)\, dx}$.

\medskip

\noindent c) Compute ${\int_2^3 x dx}$.

\medskip

\noindent d) Compute ${\int_2^3 x T''(x)\, dx}$.
{\sevenrm Don't look at b) and c)! Integrate by parts.}

\medskip

\noindent e) Compute ${\int_2^3 x^2T'''(x)\, dx}$.
{\sevenrm And again and again.}


\vfil\eject\end