(35S) Quick integration

[Roberto Volpi]

(11-14-2022 02:50 PM)J-F Garnier Wrote:  

(11-12-2022 03:56 PM)Roberto Volpi Wrote:  here a short and quick example.

f(x)=∫√(1+4X^2)dx in interval [0,1]

With the native HP35S integrator, after approx 1 minute and 37 seconds:
=1.47894285754

With this program, after 1 second:
=
stack y: 0.5
stack x: 1.48215537045

Please take into account that also the value of the native HP35S integrator is approximate.

Your comparison with the HP-35S integration full 12-digit result is not fair.
On my HP-35S using the built-in integration and the default FIX 4 display, I get 1.4789 in about 3s.
If you need even less accuracy, you can use FIX 1 or FIX 2, or better SCI 1 or SCI 2 to specify a relative target accuracy.

(11-12-2022 05:29 PM)Roberto Volpi Wrote:  Any proposal for the HP35S?

It would really be a nice challenge make a shorter and hence quicker programme.

So here is mine (enter the integration limits on the stack):
LBL I
SCI 2 ; set target accuracy
FN= F ; select function
∫FN d X ; compute the integral
FIX 4 ; restore your preferred display mode
RTN

J-F

Your proposal is pretty interesting.

In this way we don't even need to upload a programme: we just fix 3 or 4 decimal figures accuracy and the native HP35S integrator become much much faster.

As for me, the suggestion of Thomas Klemm is still valuable because it permits numerical calculation as those given in the example, with f(x)= sinX/X interval [0,2] that native integrator may not process.

We are putting together lot of interesting details...