**How to Run the Mathlet**
The mathlet has three modes that are chosen from the drop down menu
located under the right window: *Demo examples,
User defined function, User drawn function.*

*The Demo Examples mode* illustrates
the accumulated rate of change when a graph of the rate of change is
given. The right window shows a graph of the rate of change of a population
of bacteria, r(t), measured in thousands of bacteria per day, in the
time interval from 0 to 20. The time, t, is measured in days, the population
of bacteria, P(t), in thousands of bacteria. The initial population,
P(0), is given in a box located between the two windows. Given a graph
of the rate of change and the initial population, you are encouraged
to sketch in the right window a possible graph of the population P(t)
over the same time interval from 0 to 20. (You can graph in the window
by dragging the mouse with the right mouse button depressed.) The
Erase Sketch button can be used to erase the hand-drawn graph
in order to sketch a new graph. The actual graph of the population P(t)
is displayed by dragging the blue button of the
slider located below the right window. The button Next
Example provides a different graph for the rate r(t).

*The User Defined Function mode*
allows you to enter a formula for a function f(x). A function f(x) is
entered in the input box below the right window. The syntax for doing
so is the same as that used by most graphing calculators. All of syntax
rules, as well as a list of available functions, are displayed by mousing
over the button marked SYNTAX. You can
choose the x- and y-ranges in the left window, as well as the y-range
in the right window. (The x-range is the same in both windows.) The
initial value for F(x), F(a) = b, at a point (a,b) can be
entered in the box located between the two windows. After entering the
data, press the GRAPH button. The graph
of f(x) will appear in the left window. Again, you are encouraged to
sketch the antiderivative F(x) in the right window. The actual antiderivative
F(x) will be displayed by dragging the slider with the mouse. The RESET
button clears the board and resets the ranges.

*The User Drawn Function mode* lets
you draw a function f(x) in the left window rather than specify a formula
for it. This function may be piecewise continuous. You can choose x-
and y-ranges, as well as the initial value for the antiderivative, F(a) = b,
similarly to the previous option. Then the ENTER
button must be pressed to register the entries. As in the other options,
you can attempt to sketch F(x) and then display a (possibly more accurate)
picture of F(x) by dragging the slider. The ERASE
button clears the board and resets the ranges.