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\begin{tabbing}
\hskip36pc \= Math.\ 301-02\\
\>Summer, 2005\\
\>R. B. Kearfott
\end{tabbing}
\begin{center}
\bf First Examination \\
\it Wednesday, June 15, 2005
\end{center}

\noindent {\small {\bf Instructions:} This exam should be done on
your own paper. Your name should be on each sheet and on the back
of the last sheet; the answers should appear written carefully and
in order. If in doubt, show intermediate steps: Full credit may
not be given, even for correct answers, unless work is arranged
clearly and explained. This exam is closed book. You may leave
after handing in your exam paper, but be sure to check your
answers carefully. You may keep this exam sheet.}

\begin{enumerate}
   \item  (20 points) \label{prob:construct-antiderivative}
          If $F'(x)=f(x)$ is as in the graph in
          figure~\ref{fig:prob-construct-antiderivative}, and
          $F(0)=0$, then draw a corresponding graph of $F(x)$.
          Be sure to label the axes on your graph.
\begin{figure}[h]
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\put(130.00,80.00){\makebox(0,0)[cc]{$x$}}
\put(40.00,129.00){\makebox(0,0)[cc]{$f(x)$}}
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\put(35.00,50.00){\makebox(0,0)[cc]{$-3$}}
\put(35.00,60.00){\makebox(0,0)[cc]{$-2$}}
\put(35.00,70.00){\makebox(0,0)[cc]{$-1$}}
\put(35.00,90.00){\makebox(0,0)[cc]{$1$}}
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\caption{\label{fig:prob-construct-antiderivative}The figure for
problem~\protect{\ref{prob:construct-antiderivative}}}
\end{figure}
   \item (5 points apiece) Compute the following antiderivatives.
   $$\begin{array}{rlrlrl}
     \mbox{(a)} & \displaystyle \int x^2 + 2x + 1 \/dx \qquad&
     \mbox{(b)} & \displaystyle \int (x+1)^2 \/dx \qquad&
     \mbox{(c)} & \displaystyle \int 2x \sin\left(x^2\right) \/dx
     \\ \\
     \mbox{(d)} & \displaystyle \int t^2 e^{t} \/dt \qquad&
     \mbox{(e)} & \displaystyle \int x \ln(x)\/dx \qquad&
     \mbox{(f)} & \displaystyle \int \frac{1}{(x+1)(x+2)}\/dx
   \end{array}$$
   \item (20 points) Compute the area bounded by the graph of $y=x^2+2x+1$,
         the  $x$-axis, and the lines $x=0$ and $x=2$.
   \item (30 points) A 727 jet needs to be flying 200 mph to take off.  If it
         can accelerate from 0 to 200mph in 30 seconds, how long
         must the runway be?  (Assume constant acceleration.)
\end{enumerate}
\end{document}
