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\begin{center}
{\Large Warm-Up Problems and Lecture Problems

March 14, 2003}
\end{center}

\begin{enumerate}

\item   Consider the triangle with vertices $(0,0)$, $(1,2)$ and $(1,0)$.
	\begin{enumerate}
	\item  Find the equation of the line between $(0,0)$ and $(1,2)$.

	\item  Rotate this triangle about the line $y=0$ (the $x$-axis) and set up an integral representing the volume of revolution.  Draw the picture too!

	\item  Rotate this triangle about the line $y=4$ and set up an integral representing the volume.  Draw the picture too!

	\item  Rotate this triangle about the line $x=0$ and set up an integral representing the volume.  Draw the picture too!

	\item  Rotate this triangle about the line $x=5$ and set up an integral representing the volume.  Draw the picture too!

	\end{enumerate}


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\lecture

\item  Sketch the graph of the parametric equation for $-2\leq t \leq 3$:
	\[
	x=t^2-2t \qquad y=t+1
	\]

	\item  Set up an integral representing the length of the curve:
	\[
	x=t^2 \qquad y=e^{t} \qquad 1 \leq t \leq 4
	\]

\end{enumerate}

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