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\textbf{\hfill Math 220 -- Quiz 13 (take-home)} \\
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\textbf{Name}\ \rule{3.5in}{.4pt} \hfill \\[0.3in]
\textbf{TA/Section}\ \rule{3.1in}{.4pt} \hfill
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\begin{itemize}
\item You can use calculators, textbooks, notes, other students, etc.
\item This quiz is due by 4:00PM Friday in your TA's mailbox in 250 Altgeld Hall.
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\begin{enumerate}
\item (2 points) A spring has a natural length of $2$ $m$. A force of $24$ $N$ stretches the spring to a length of $2.4$ $m$. Starting at its natural length, how much work will it take to stretch the spring to a length of $2.6$ $m$ ?
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\item (2 points) Find the average value of the function $\D{f(x)=5\sin{\left(\frac{x}{2}\right)}}$ on the interval $[0, 2\pi]$.
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\item (3 points) Let \textbf{R} be the region bounded by the $x$-axis and the graph of $\D{y=x^3-9x}$ on the interval $[0,3]$. Set up, but do not evaluate, a definite integral for the volume of the solid obtained when \textbf{R} is revolved around the line $x=5$.
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\item (3 points) An inverted conical tank has a $2$ foot radius at the top and is $6$ feet high. It is filled to a height of $5$ feet with olive oil weighing $57$ $lb/ft^3$. Set up, do not evaluate, a definite integral which represents the amount of work that it takes to pump the oil to a point $1$ foot above the top rim of the tank.
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\end{enumerate}
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