🚀 go-pugleaf

On Mon, 19 Dec 1994, David J. Peters wrote:

> I am very new to the TI-82, but since the "CALC" menu allows you to find
> the integral of a function between two x values (although it doesn't want
> to when you plot something from the CBL), would it possible to have the
> calculator do a curve fitting which creates a function which approximates
> your data (could be tedious)?  Then you could calculate the integral from
> the "CALC" menu.
>
> Let me know if you make any progress.  I am VERY interested in the
> capabilities of the CBL for just such an activity.
>
> Dave Peters, Physics Teacher
> East Kentwood High School
> 6178 Campus Park SE
> Kentwood, MI  49508
>
>
>
> On Mon, 19 Dec 1994 Tbross@aol.com wrote:
>
> > Could anyone suggest how to find, on a TI-82, the area under a curve, a
 curve
> > that is not part of a defined function?  Using a CBL and a force sensor I
> > have recorded the collision of a cart with the sensor and plotted force vs.
> > time.  I would like to compare the change in momentum with the area under
 the
> > curve.
> >
>

Regarding the desire to find the area under the curve for graphs generated
by the CBL.  I suggested fitting a curve to the data points and then using
the integral feature of the CALC menu.  My "intuitive" guess was just what I
remembered from an article I read which was described in the Fall 1994
(Vol. 4, No. 1) issue of "Eightysomething".  I have since found the
article and tried the procedure.  It seemed to do the trick.  Here is a
paraphrased version of what the article described.

The data points used to produce the CBL graph are stored in lists which
can be viewed by pressing STAT and then pressing ENTER, or by selecting 1,
to choose EDIT.  Look at the lists to determine where the x and y data are
stored for the program you were using with the CBL.  (in the request these
were time and force)

Then, press STAT and select <CALC>.  The display shows a variety of curve
fitting calculation choices.  For the data I used from the CBL I chose
ExpReg which entered the command ExpReg on the normal display screen.  The
arguements to follow the command are L (sub x), and L (sub y) where sub x
and sub y refer to the number of the lists where the appropriate x and y
data are stored. (Entered from the keyboard using 2nd then the list
variable/subscript (in blue above the keys)).  These must be separated by
a comma.  Press ENTER.  The calculator then works for a bit and returns the
appropriate constants for the curve fitting calculation you selected.

You can now transfer this information to the Y= menu.  Select Y= and clear
out any previously entered equations.  Press VARS, choose 5: Statistics,
use the arrow key to highlight EQ, and choose 7:RegEq.  The equation will
appear in the Y= listing.

Now press GRAPH.  The equation you just transferred to the Y= menu will be
graphed as a continuous graph along with your original data points.  If
the selection of the curve fitting routine was appropriate, the graphs
should agree fairly well.

To find the area under the curve press CALC and select the integral of
f(x) dx which will take you to a cursor which traces the continuous graph.
Cursor to an appropriate point and press ENTER to select the lower bound.
Now cursor to the upper bound and press ENTER to select it.  The area will
be shaded in and the value for the area will be displayed.  (This is
way cool!)

Let me know if this works for your situation.