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\begin{document}
\begin{center}

\Huge{Area between Curves}\\
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\normalsize
\noindent Recall is the graph of $f$ is given as below then $\int_a^b f(x) \,dx$ corresponds to the area shaded below.

\begin{center}
\includegraphics[height=2in]{FforAreaWks}	
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\begin{enumerate}
\item Let $g$ and $h$ have the graphs below.

\includegraphics[height=1.5in]{GforAreaWks}	\includegraphics[height=1.5in]{HforAreaWks}	

\begin{enumerate}
\item Find $\int_{-2}^2 g(x)\, dx$.
\vfill
\item Find $\int_{-2}^5 g(x)\, dx$.
\vfill
\item Find $\int_{-2}^2 h(x)\, dx$.
\vfill
\item Find $\int_{-2}^5 f(x)\, dx$.
\vfill

\newpage
\begin{center}
\includegraphics[height=2in]{GHforAreaWks}	
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\item Consider the area bounded between $g$ and $h$.  Use your work in (a) and (c) to find the area bounded between $g$ and $h$ from $x=-2$ to $x=2$.

\vskip 1in

\item Use approximating rectangles with $\Delta x$ equal to .5 and approximate the area in part (e).  How did you find the height of the rectangles?  How would you find the height of the rectangles if you weren't given the graph but only the rules of $g$ and $h$?
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\item Write the area you calculated in part (e) with integral notation.
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\noindent Verify your answer by looking at the figure on page 252.
\item Find the area bounded between $g$ and $h$ from $x=2$ to $x=4$.  
\vskip 1in
\item Will the same formula (but with the limits of integration moved appropriately) still work to calculate this area?  i.e. is the area you calculated in part (h) still represented by $\int_2^4 g(x)-h(x) \,dx$?



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\end{enumerate}







\end{enumerate}
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