TOPIC: fnInt function
     PRODUCT:  TI-85
     DATE: May 6, 1993

     Recent postings have touched on the operation of fnInt and the
     possibility that the response might be slow enough to suggest that
     the function is not working.  The main thing to check for is
     the value of "tol" under the TOLER menu.  This is an absolute error
     limit that the algorithm is asked to meet.  For instance, a value of
     1E-9 would be trying to achieve 9 accurate digits after the decimal
     point in the result, which takes quite a lot more work than, say, 2
     or 3 total accurate digits.

     It may be helpful to realize that a graph does not need to be more
     acccurate than one pixel to "look" right.  Obviously, this depends on
     the Y-range, but for "typical" plots a "tol" of .01 is conservative.
     In fact, because the integration for "smooth" functions usually turns
     out to be more accurate than the requested tolerance by a few orders
     of magnitude, you can usually get visually correct plots with "tol" as
     large as 1.  A large "tol" like 1 does increase graph speed noticeably
     for y= functions using fnInt. However, be aware that under some
     conditions, the integrator can simply "lose it" with a very large
     tolerance, so be alert if you do this!

     The method posted by Bert Waits (using parametric mode) is quite
     effective because the selection of the tstep size allows you to
     control a certain amount of straight line interpolation, which
     reduces the number of full integrations on the screen.  You can
     trace this result easily, but the integrand is recomputed (once)
     each time you trace to a new t.

     Another approach may be helpful if you do this type of operation
     frequently, using the following program.  To plot an equation and
     the integral, enter the equation as one of your "y=" equations,
     then run the program and enter the number of the equation at the
     prompt "Equ?".  For instance, if your equation is y7, enter 7.
     You are prompted for the number twice because the TI-85 has no
     number to string conversion.  Then the program will plot the 
     equation and compute the integral "point by point" across the
     screen.

     The integral is computed between pixels and added to the integral at
     the previous pixel, rather than computing the integral from xMin to
     the pixel to be plotted each time, thereby saving time.  More
     importantly, the results are put into a list (named Lst), and a
     new equation (y99) is created to plot this list.  Finally, the
     selected equation and y99 are plotted.  You can change the Y-range
     and also trace the integral easily.  If you change the X-range,
     however, you will need to run the program again, because you have
     changed the limits of integration.

     Note that the program does not set the value of "tol", so make
     sure that tol is appropriate.  To set "tol" from the program,
     a value of (abs(yMin - yMax) / 100) would be appropriate if
     you don't plan to change the Y-range too much while viewing the
     plot.

\START\
\COMMENT=Program file dated 05/11/92, 08:58
\NAME=PLTINT
\FILE=PLTINT.85P
ClLCD
{0}\->\Lst
Input "Equ?",No
InpST "Equ?",NoSt
"y"+NoSt\->\NoSt
\St>Eq\(NoSt,Ieqn)
FnOff 
FnOn No
0\->\IGL
For(Ndex,1,127)
(xMin+Ndex*\Delta-x\)\->\x
(IGL+fnInt(Ieqn,x,x,x+\Delta-x\)\->\IGL
IGL\->\Lst(round((x-xMin)/\Delta-x\,0)+1)
PtOn(x,IGL)
End
xMin\->\xmin
y99=Lst(round((x-xmin)/\Delta-x\,0)+1)
\STOP\

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