Problems of HP prime with triple integrals?

05312020, 07:41 AM
Post: #1




Problems of HP prime with triple integrals?
Hi,
I tried to compute the following triple integral: integral(integral(integral(e^(x²+y²/2+1/z))dz)dy)dx with the following limits: x: 0.,1.; y:0.,2.; z:1.,4. Screenshot of the HP prime Pro software is attached. I tried it with the HP Prime Pro PC software and with a HP prime G2. None delivered a solution within half an hour. The TInspire CX IIT CAS came to the solution 17.147920 within 1 or 2 seconds. Even my old TI89 titanium showed the same solution within 10 seconds. Does the HP prime have problems with triple integrals or is there something I am doing wrong? Thank you very much and best regards Raimund Wildner 

05312020, 09:38 AM
Post: #2




RE: Problems of HP prime with triple integrals?
Any calculator will have trouble with triple integrals that don't factorise into a product of singlevariable integrals. To evaluate such an integral numerically to a high degree of precision requires of the order of \(N^3\) points, compared with \(N\) points for similar precision for a singlevariable integral.
Your integral factorises, so calculators that spot this can evaluate it rapidly. The Prime doesn't appear to check for this, so it evaluates the integral the long way. I would guess that for multiple integrals that don't factorise the Prime and TI NSpire would be comparable, with the Titanium way behind! Having said that, I am surprised that the Prime didn't finish at all. Perhaps there is a problem. Nigel (UK) 

05312020, 10:54 AM
Post: #3




RE: Problems of HP prime with triple integrals?
Strange. If I change variables to \(u=1/z\), then with exact mode ticked and approximate evaluation I get the correct answer to the triple integral at once, after a couple of messages.
With exact mode not ticked I get a message about using Romberg, then the calculator carries on calculating until interrupted. With \(1/z\) in the exponent I can't get an answer to the triple integral at all, although the equivalent single integral evaluates with no problem. Something's not right! Nigel (UK) 

05312020, 01:21 PM
Post: #4




RE: Problems of HP prime with triple integrals?
(05312020 10:54 AM)Nigel (UK) Wrote: Strange. If I change variables to u=1/z, then with exact mode ticked and approximate evaluation I get the correct answer to the triple integral at once, after a couple of messages. With u=1/z, integral is trivial to evaluate, with integration by parts \(\large \int e^{1\over z}\;dz = \int e^u\;d({1\over u}) = {e^u \over u}  \int {1 \over u}\;d(e^u) = {e^u \over u}  Ei(u) \) 

05312020, 04:04 PM
Post: #5




RE: Problems of HP prime with triple integrals?
The TINspire CX 2 (non CAS) also manages to report the correct answer...
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05312020, 04:10 PM
Post: #6




RE: Problems of HP prime with triple integrals?
(05312020 09:38 AM)Nigel (UK) Wrote: Having said that, I am surprised that the Prime didn't finish at all. Perhaps there is a problem. Hi Nigel, thanks a lot for your answer. HP prime really seems to have a problem here. I tried it once more and after about an hour there came a message like "A problem occured to HP Prime and it will switch off in 3 seconds". Then it switched off. If switched on again everything is normal, no message. So normally you will not see it. So I think I have to program it step by step, e.g. using Gauss' or Romberg's method. Best Raimund 

01072021, 07:23 PM
Post: #7




RE: Problems of HP prime with triple integrals?
It's easier to compute the product of 3 integrals
Code: int(exp(x^2),x,0,1)*int(exp(y^2/2),y,0,2)*int(exp(1/z),z,1,4.0) 

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