Improper Integrals with the HP-15C LE & CE

[J-F Garnier]

(11-13-2023 03:00 PM)Namir Wrote:  intgeral of 1/sqrt(x) for x = 0 to 1 (accurate solution is 2)
HP-15 LE gave 1.9998705
HP-15C CE gave no solution

intgeral of cos(x)*log(x) for x = 0 to 1 (correct is -0.9460830703670)
HP-15C CE gave -0.946082894
HP-15C LE gave -0.946083028 (slighly more accurate)

I'm 99.99999999% sure that the LE and CE give the same results, since they use the same ROM (except for the extended memory patches, if you use the CE/192 mode).

You didn't mention an important condition to check your results, however I can give the result I got on the 15c HP emulator (2012) thanks to its fast speed and close simulation of the 15c LE :
in FIX 7, first integral is 1.9999997 with an error bound of 0.0000001.
This is indeed a case where the error estimation is inaccurate, still the result isn't that bad.

BTW, it's a major benefit of the Romberg algorithm to provide an error bound.

J-F