Sharp EL-W506T vs. Sharp EL-W516T

[Pjwum]

(11-15-2019 01:50 AM)Mjim Wrote:  I tried this myself, but I kept getting different results.

Xcas: 6.25630506563*10^10
Casio fx-9750GII: 6.256305066*10^10
Casio fx-570MS (upgraded temporarily from a fx-82MS): Throws math error.
Sharp EL-W516X:
-Default divisions: 1.54840203*10^17
-1024 divisions: 6.694153651*10^10
-4096 divisions: 6.258289041*10^10
-32768 divisions: 6.251558833*10^10 (This took a very...very long time)

Not sure if these results are right; might of made a mistake with some units somewhere.

Mjim, your result is correct. I messed up km and m.

(Of course 1/r^2 converges and so does the indefinite integral over 1/r^2 from rE to inf. Express the energy to bring a mass probe from Earth to infinity in space as kinetic energy at rE and you get the so called escape velocity which is independant from the mass probe (11.2 km/s for our planet)).

1/r^2 drops really fast and is reduced to 1/10th at about 1/20th the distance to the moon or 0.05 light seconds from Earth. Poor EL-W506 takes its default Simpson n=100 and averages the first trapezoid over a distance of 1/100 ly = 315360 light seconds, which results in a huge error right from the start.

As far as I have seen the Sharp doesn't offer default settings for its integration algorithm, as Bob asked. You have to - optionally - make an educated guess for n every time you start an integration instead of specifying your required eps. Of course this is beyond any high school level.

Patrick