Hp50 'Integral (0,infinity,SIN(X)/X,X)' gives 5.04540304996

[Gil]

With the HP50G EMU48

'Integral (0,infinity,SIN(X)/X,X)' gives 5.04540304996,
but the correct answer should be pi/2.

How can I get the correct answer on the HP50G (EMU48)?

Thanks for your help.

[Martin Hepperle]

Did you set angle mode to "radians"?

[Gil]

Yes, Radian mode set, but with degrees exactly the same wrong result, after about 23" of calculation with EMU48 on my Samsung phone.

Just for information, with HP50G:
integral of (0,100,SIN(X)/X,X)' —> 1.56222546689
integral of (0,400,SIN(X)/X,X)' —> 1.57211486927
integral of (0,10000,SIN(X)/X,X)' —> 1.57089154534
integral of (0,1000000,SIN(X)/X,X)' —>1.5762385912
and integral of (0,1000000000,SIN(X)/X,X)'
—>1.31094565782.

Besides:
Integral of (0,2*pi,SIN(X)/X,X)' —>1.41815157613
and integral of (2*pi,infinity,SIN(X)/X,X)' —> -1.91522972303;
adding those two areas: -.4970781469.

[Martin Hepperle]

I agree, the angle mode should make no difference in this case.

On a HP 49G and HP 50g this takes a long time but yields 1.55488... for a reduced upper bound of 20*pi resp. for 10*360 in degrees mode.

I am not sure whether the integration finishes in finite time for an upper limit of infinty on the real calculators.

[Gil]

In fact integral (0,infinity,SIN(X)/X,X) takes — with final wrong result — about 23.3" to calculate with EMU48 on my Samsung phone A53.

On the real calculator, the wrong output should be given, I suppose, after 100×23.3", or after about 34'-39'.

[C.Ret]

(12-13-2024 11:00 AM)Gil Wrote:  Just for information, with HP50G:
integral of (0,100,SIN(X)/X,X)' —> 1.56222546689
integral of (0,400,SIN(X)/X,X)' —> 1.57211486927
integral of (0,10000,SIN(X)/X,X)' —> 1.57089154534
integral of (0,1000000,SIN(X)/X,X)' —>1.5762385912
and integral of (0,1000000000,SIN(X)/X,X)'
—>1.31094565782.

Just for information, with HP Prime (in radian mode):

All results displayed in a few milliseconds only on the G1 hardware.

[Gil]

Impressive — and a "pity" for the HP50G.

[Martin Hepperle]

... indeed, on the real 50g hardware I also obtained 5.04540304996 for the range 0...2*pi after about 30 minutes. So the simulator is "correct".

The HP 49G says 1.55488887105 for the same range.

Maple:
0...2*pi -> 1.418151576
2*pi ... oo -> 0.152644751

It is "funny" that the error seems to come from the higher x-values, where the function behaves better than around x=0.

Nice to see, that the Prime has the Si(x) integral in its CAS rules.