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1.)  Find the area between the curve 
$f(x) = \left\{\matrix{ 2 & x < 0 \cr 
		-3 & x > 0}$, 
and the x-axis, and between $x = -4$ 
and $x = 5$.

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2a.)  $\int_{-4}^5 |f(x)|dx = $
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2b.)  $\int_{-4}^5 f(x)dx = $
\w
\eject
3.) The speed of a runner decreased steadily after crossing the finish 
line.  Her speed at 2 second intervals is given in the table.  Find lower 
and upper estimates for the distance that she traveled during these 6 
seconds.
$$\matrix{  t(seconds) & 0  & 2 & 4 & 6 \cr
         v(feet/sec)& 40 & 20 & 5 & 0}$$


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\centerline{Lower estimate: $\underline{\hskip 1in}$, ~~ Upper estimate: 
$\underline{\hskip 1in}$}



\includegraphics[width=20ex]{grapht}
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\includegraphics[width=20ex]{grapht}


\eject

FYI:  Side Note:

A.)  Find the area under the curve $f(x) = 2$, above the x-axis, and 
between $x = 0$ 
and $x = 5$.
\vfill

\vfill

B.)  Find the area under the curve 
$h(x) = \left\{\matrix{ 2 & x \not= {1}, 2, 3, 4 \cr 
		0 & x = {1}, 2, 3, 4}$, 
above the x-axis, and between $x = 0$ 
and $x = 5$.


\vfill

C.)  Find the area under the curve 
$h(x) = \left\{\matrix{ 2 & x {\hbox{ irrational}}\cr 
		0 & x {\hbox{ rational}}}$, 
above the x-axis, and between $x = 0$ 
and $x = 5$.


\vfill

D.)  Find the area under the curve 
$h(x) = \left\{\matrix{ 2 & x {\hbox{ rational}}\cr 
		0 & x {\hbox{ irrational}}}$, 
above the x-axis, and between $x = 0$ 
and $x = 5$.


\vfill


${1 \over 1}, {1 \over 2}, {2 \over 1},  {1 \over 3}, {3 \over 1},  {1 
\over 4},  {2 \over 3}, {3 \over 2}, {4 \over 
1}, ...$

\end
