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\begin{center}
{\Large TEST 1

Math 202}
\end{center}

\begin{itemize}
\item  Show all your work and make your work neat.  You will be graded on these things!
\item  Do your work on separate paper (you don't need to turn this sheet in).
\item  You can use a calculator, but I must be able to follow your work as if you had no calculator.
\end{itemize}



\begin{enumerate}


\item  (20 points)  Find the following integrals
\begin{enumerate}
\item  \[  \int_0^1 xe^{-x^2} \; dx \]
\item  \[  \int x^2 e^{x} \; dx \]
\item  \[  \int_0^{\pi/3} \frac{\sin \theta}{\cos^2 \theta} \; d\theta \]
\item  \[  \int x^5(4x^6-17)^{10} \; dx \]
\item  Find the following integral
\[
\int_{-2}^{2} \sqrt{4-x^2} \; dx
\]
Hint: think about areas.
\end{enumerate}


\newpage

\item (10 points)  Consider the curves $y=2x$ and $y=-x^2+6x$.
Find the area between these curves.

\item (10 points)  Consider the curves $y=2x$ and $y=-x^2+6x$.
Take the area enclosed between these curves and rotate it around the line $x=-1$.
Write an integral to represent the volume of this solid.
\\
Extra credit (2 points): Compute the integral.


\item (10 points)  Consider the curves $y=2x$ and $y=-x^2+6x$.
Take the area enclosed between these curves and rotate it around the line $y=-1$.
Write an integral to represent the volume of this solid.
\\
Extra credit (2 points): Compute the integral.



\item (10 points)  Find the average value of the function $f(x)=\cos x$ on the interval $[0, \pi/2]$.
Describe what this means in terms of the graph of $\cos x$.




\end{enumerate}

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