Comments and discussion on Valentin's 4th "Then and Now" - Area

[J-F Garnier]

(01-21-2023 03:53 PM)Albert Chan Wrote:  

(01-21-2023 10:15 AM)J-F Garnier Wrote:  In that way, it is possible to concentrate the samples in the regions that need them, and avoid wasting time with useless samples in the other regions.

This is what HP Prime integrate does, by zeroed-in to the region that need them.
However, this adaptive routine does not work well with fuzzy numbers. (see here)

I had the idea that it may be possible to write an adaptive integration code on the 71B by first analysing the integrand behaviour, actually I'm surprised not to find anything like that in the forum or various 71B code archives (I didn't do a extensive search though). Maybe is it just too complex, or just with no real usage.

(01-11-2023 10:17 PM)Albert Chan Wrote:  Let a = 0.831971149978, a+b = a+B/2 = 2.82740261413
Infinite slopes at y = 0 and a, moved to z = 0

Area = \(\displaystyle \int_0^{a+b} f(y)\;dy
= \int_0^{1/2} \Big[\big(f(a\,z) + f(a- a\,z)\big)·a \;+\; f(a+B\,z)·B\Big] \,dz
\)

I read this part of your posts, but honestly didn't understand how you devised the RHS expression from f(y).
I guess this is classic math, but after all Valentin's challenges have always been the right place to learn something, so if you could explain it a bit, it would be appreciated.

J-F