Integration: TI-86 & Casio Algebra 2.0 Plus

[carey]

(03-27-2024 07:58 PM)Steve Simpkin Wrote:  For reference, here are a few timings and results for integrating the above problem using some of the calculators I had handy. The Casio fx-991EX is the only one that gave an error if I used the limits of 0 to 1.

Model, lower limit, upper limit, timing = result
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HP Prime (simulation), 0, 1, instant = 1.02576051093
Casio fx-CG50, 0, 1, 2.5 seconds = 1.025760511
Casio fx-991EX, .0001, .9999, 16 seconds = 1.025521692
HP 35s, 0, 1, (FIX 4) 7 seconds = 1.02574948999
HP 35s, 0, 1, (FIX 5) 14 seconds = 1.02575840691
HP 35s, 0, 1, (FIX 6) 45 seconds = 1.02576041372
HP-48G, 0, 1 4.5, (fix 5) 4.5 seconds = 1.02575840691
HP-48G, 0, 1 4.5, (fix 7) 29 seconds = 1.02576049152
TI-89, 0, 1, 18 seconds = 1.0257605126

Thanks Steve, this is very helpful! It’s also very telling that the only two cases of integration hiccups with this composite trig function are both Casio models (Algebra 2.0 & 991EX), yet the Casio CG50 (and also CG500) handle it fine.

For a comparison of digits, here’s Wolfram Alpha’s result: 1.025760510931330450398548660969552795334871856215069394223386844015851920899070​94222678787919779530713296457148872019952569383155579574734512368046551

It looks like the HP Prime’s result is closest to Wolfram’s Alpha’s result. Since this numerical integration is obtained iteratively and the Prime is the fastest of the lot, I wonder if that’s part of the reason the Prime reaches greater accuracy by the time it reports its result.