%% Math 132 Midterm 1, Spring 2005
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\begin{document}

\begin{center}

\textbf{College of the Holy Cross, Fall Semester, 2004} \\
\textbf{Math 132, Midterm 1} (All Sections) \\
\textbf{Wednesday, February~23, 6 PM}
\end{center}

\vfil

\noindent\textbf{Name}: \Blank
\vskip 0pt plus .3fil

\paragraph{Instructions} Please write your answers in the spaces
provided, and show work on the test itself. Use the back of the
preceding page if you need more space for scratch work.

\vfil

\noindent\textbf{Please do not write in the space below}

\begin{center}
\begin{tabular}{|l||r|}
\hline
Problem & Points/Poss    \Strut \\
\hline\hline
1  & \hfil/\  20\hfil \Strut \\
\hline
2  & \hfil/\  10\hfil \Strut \\
\hline
3  & \hfil/\  10\hfil \Strut \\
\hline
4  & \hfil/\  20\hfil \Strut \\
\hline
5  & \hfil/\  20\hfil \Strut \\
\hline
6  & \hfil/\  10\hfil \Strut \\
\hline
7  & \hfil/\  10\hfil \Strut \\
\hline\hline
Total   & \hfil/100\hfil \Strut \\
\hline
\end{tabular}
\end{center}

\vfil\eject

\begin{enumerate}
  
\item{} [5~points each]\quad Compute the following:

  (a) $\ds\int 2x(x^2+5)^{7/2}\,dx$
  \vfil\sep

  (b) $\ds\int \sin(3\theta)\,d\theta$
  \vfil\sep

  (c) $\ds\int\frac{dx}{2x+1}$
  \vfil\sep

  (d) $F'(x)$, where $F(x)=\ds\int_\pi^x\frac{t}{1+\sin^2t}\,dt$
  \vfil\eject
  
\item{} [10~points]\quad The graph $y=f(x)$ is shown. Let~$F$ be the
  antiderivative of~$f$ satisfying $F(2)=0$. Find the indicated values, 
  and carefully sketch the graph $y=F(x)$ in the grid provided.
  \[
  F(1)=\Blank\qquad
  F(3)=\Blank\qquad
  F(4)=\Blank\qquad
  F(6)=\Blank
  \]

  \begin{center}
    \input{midterm1a.eepic}
    \input{midterm1b.eepic}
  \end{center}

\vfil\eject

\item{} [5~points each]\quad A drag racer accelerates at
  $a(t)=(20+t)~\mathrm{ft/sec}^2$.
  
  (a) How fast is the car traveling after 6~seconds? (The car is
  initially at rest.)

  \vfil
  \Answer{Speed:}
  \sep

  (b) How far has the car traveled after 6~seconds?

  \vfil
  \Answer{Distance traveled:}
  \eject
  
\item{} [10~points each]\quad Find the integrals. Use the indicated
  method to get started.

  (a) $\ds\int_1^4\frac{\sqrt{1+\sqrt{x}}}{\sqrt{x}}\,dx$
  (Substitution)
  \vfil\sep

  (b) $\ds\int t\sec^2 t\,dt$ (Integrate by parts)
  \vfil\eject

\item{} [10~points each]\quad Compute the integrals

  (a) $\ds\int\frac{dx}{(4-x^2)^{3/2}}$
  \vfil\sep

  (b) $\ds\int\frac{dx}{x^2+4x+8}$
  \vfil\eject

\item{} [10~points]\quad Find the indefinite integral
  $\ds\int\frac{x^2+1}{x(x+2)(x-1)}\,dx$
  \vfil\eject
  
\item{} [10~points]\quad Compute any \textbf{two} of the following;
  clearly mark your choices and indicate the method of integration.
  \[
  \mathrm{(i)}\ \int\frac{1}{\sqrt{1-x^4}}\,dx\qquad
  \mathrm{(ii)}\ \int\frac{x}{\sqrt{1-x^4}}\,dx\qquad
  \mathrm{(iii)}\ \int\frac{x^2}{\sqrt{1-x^4}}\,dx\qquad
  \mathrm{(iv)}\ \int\frac{x^3}{\sqrt{1-x^4}}\,dx
  \]

\vfil

\end{enumerate}

\end{document}
