HP71B Integral Questions

[Wes Loewer]

(02-07-2020 08:23 AM)J-F Garnier Wrote:  

(02-07-2020 03:49 AM)Wes Loewer Wrote:  The 50g definitely uses Romberg extrapolation of midpoints.
...
I could be wrong, but I would be very surprised if they changed up the algorithm for the 71b.

It's easy to check that the HP71 doesn't use the mid points but the trapezoid nodes, by tracing the function sampled points:

10 DEF FNF(X) @ PRINT X; @ FNF=X @ END DEF
20 I=INTEGRAL(-1,1,.00001,FNF(IVAR))

>RUN
0 -.6875 .6875 -.3671875 .3671875 -.9140625 .9140625
the sampled points corresponds to the u values of 0, +/-0.5, +/-0.25, +/-0.75.

Yes, those are the points that you would expect using midpoints. These are the same points used on the 50g.

n=1: the rectangle goes from -1 to 1 with a midpoint at 0
n=2: rectangles go from -1 to 0 and 0 to 1 with midpoints at -0.5, 0.5
n=4: rectangles go from -1 to -0.5, -0.5 to 0, 0 to 0.5, and 0.5 to 1 with midpoints at -0.75, -0.25, 0.25, 0.75