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{\bf Math 172 Quiz 2} \hfill {\bf Name:} \underline{\hspace{2in}}

Sections: 6.2-6.3  \hfill Point values in \boxed{\text{boxes}}.

25 January 2019 

Consider the region $R$ bounded by the graphs of $y=2x$ and $y=x^2$.

\begin{enumerate}
\item \boxed{1} Carefully sketch the region $R$.
\begin{center}
 	\begin{tikzpicture}
	\draw[step=0.75cm,gray,very thin,dashed] (-1.5,-1.5)grid (4.5,4.5);
	\draw[thick,->] (-1.5,0) -- (4.5,0);
	\draw[thick,->] (0,-1.5) -- (0,4.5);
	\end{tikzpicture}
\end{center}

\item \boxed{4} A solid has base given by the region $R$ and cross sections 
perpendicular to the $y$-axis are squares.  Express the volume as an integral.  
{\bf Do not evaluate.}
\vfill

\item \boxed{5} The region $R$ is rotated about the line $y=-1$.  Using the 
method of disks/washers, express the resulting volume as an integral. {\bf Do 
not evaluate.}
\vfill

\end{enumerate}



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