Integration Problem

[jte]

(09-22-2022 07:53 PM)rawi Wrote:  ⋮
This reminds me of the Handbook for the HP 34 C from 1979 where it was explained (p. 257ff) that for the integral of x*e^(-x) from zero to infinity with infinity replaced by 1*10^99 the integration routine of the HP 34C delivers the result 0, which is wrong (the correct value is 1). This function as well has only in a very narrow area values near to zero values that are numerically different from zero.

Nice example.

This thread has reminded me of a recent change (my memory isn’t quite as long!) to the Prime code base — revision 14623 for ticket 51 in the bug tracker — to improve Fcn / Intersection…’s (in Function’s Plot view) handling of F1(X)=166/75^X and F2(X)=180/97^X. Here, again, functions are tapering towards zero. (What struck me while making the change is how blithely one routinely goes from F1(X)=F2(X) to F1(X)-F2(X)=0 without considering the magnitudes of F1(X) and F2(X).)