\documentclass[fleqn, 12pt]{article}
%\pagestyle{empty}
\setlength{\topmargin}{-.5in}
\setlength{\oddsidemargin}{-.3in}
\setlength{\textheight}{9in}
\setlength{\textwidth}{7.2in}


\usepackage{amssymb}
\usepackage{amsmath}


\newcommand{\adj}{\mathrm{Adj}}
\newcommand{\mbf}{\mathbf}
\newcommand{\R}{\mathbb{R}}
\newcommand{\ra}{\rightarrow}
\newcommand{\proj}{\mathrm{proj}}
\newcommand{\dotprod}{\bullet}

\newcommand{\sol}{{\textbf{Solution: }}}

\newcommand{\lecture}{{\Large\textbf{Lecture Problems}}}

\begin{document}

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

March 17, 2003}
\end{center}

\begin{enumerate}

\item  (Review)  Rotate the region in the plane bounded by $y=x^2$ and $y=4x$ 
	around the axis $y=-5$.
	Set up an integral representing the volume of this region.

\item   Sketch the parametric curve and find the length (at least set up the integral!).
	\begin{enumerate}
	\item  $x=t^3/3$, $y=t^2/2$, $0\leq t \leq 1$.
		\\
	(Remember that the formula for arc length is $L=\int_a^b \sqrt{(dx/dt)^2 + (dy/dt)^2}\;dt$.)

	\item  $x=4\sin t$, $y=4 \cos t -5$, $0 \leq t \leq \pi$.
	\end{enumerate}


\newpage

\lecture

\item  Set up the integral representing the length of the curve (try to compute the integral if you have time -- keep in mind that you might have to use numerics).
	\begin{enumerate}
	\item  $y=e^x$, from $(0,1)$ to $(1,e)$.

	\item  $y=\frac{x^3}{6} + \frac{1}{2x}$, $\frac{1}{2} \leq x \leq 1$.

	\item  $y=\sin x$, $0\leq x \leq 2\pi$.

	\item  $x=y^4$, $-1\leq y \leq 2$.
	\end{enumerate}

\end{enumerate}

\end{document}