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\noindent
\textbf{Directions:}  
\begin{enumerate}
	\item Write your name with one character in each box below.
	\item Show all work.  No credit for answers without work.
	\item All answers should be simplified.
\end{enumerate}

\newpage
\headers{Math156 Sec 005}{Quiz 3}{Sep 4, 2026}

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\begin{enumerate}

\item\points{4} Sketch the region enclosed by the curves $y=\sqrt{x-1}$ and $x-y = 1$ and find its area.
\vfill
\item\points{3} Find the average value of the function $f(x)=xe^{x^2}$ in the interval $[1,4]$.
\vfill
\item\points{3} A parabolic dam is bounded by the equations $y=5-x^2$ and $y=0$, where $x$ and $y$ are in meters.  The water level is at $y=3$.  Given that $\textrm{Force}=(\textrm{Pressure})(\textrm{Area})$, $\textrm{Pressure}=\delta\cdot\textrm{Depth}$ where $\delta=9800 N/m^3$, give a definite integral for the force due to hydrostatic pressure on the dam.  \textbf{Do not solve the integral.}
\vfill
 
\end{enumerate}
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