Improper Integrals with the HP-15C LE & CE

[Namir]

(11-14-2023 07:27 AM)Johnh Wrote:  I tried the 1 / (sqrt x) integral on my 15C CE, and a couple of 15C emulators, with very variable results!

The real 15C CE performed the same as described above, as each FIX setting, basically 1.999.....etc

But two versions of Touch 15i for Android returned 2.012658, consistently subject to the number of digits requested, and never got nearer to 2.

The Jovial JRPN 15C doesn't seem to settle on a value, even at just 2 or 3 decimal places

I did try using HP-15C emulators with similar results.. I suspet the developers implement their preferred algorithms for numerical integration. It all comes down on how the algorithm handles the end points. The Gaussian Quadratures and Open Newton-Cotes methods do not evaluate the end points. I even tested the Trapezoidal mid-point algorithm and got goood approximations (for four decimal places) but at a whopping number of iterations!