One of the standard applications of the definite integral is to find
the area between two curves. To find the area you need to have
two curves that bound the area and limits of integration.
This can be set up where the region of integration is defined
with a top curve and a bottom curve. In this case we have a range
of integration for x. For each x we use the difference between
the top and bottom curves as the integrand.
The problem can also be set up with the area defined as going from a
left curve to a right curve with a range of integration for y.
Things to notice:
The view window for the graph is defined by the ordered pairs
The boundary curves are graphed in green. A pair of green
blue dots are graphed at the value of t0 on the low and
high curves respectively. The numeric values of these points can
be found in a readout on the control panel.
In either direction the area can be thought of as broken into
rectangles that are so thin they look like lines.
The arrows should go either from bottom to top or from left to
right. If the arrows go the other way the integrand is negative.
The value of area in the readout is found using Simpson's rule