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Improper integral - lrdheat - 06-11-2014 06:01 PM
Just got an odd result for the improper integral evaluated from 0 to 33 of 1/(5th root of x-1). It should evaluate to 75/4 or 18.75. In home, I get 18.7479519638 after a busy spell hourglass. In CAS, I get a choice of 155/4 (way off!) or 18.750007847.
The HP 39gii after awhile has ER: Invalid Input.
The TI NSpire immediately produces 75/4.
RE: Improper integral - lrdheat - 06-11-2014 06:11 PM
...and when I enter it in as the addition of 2 integrals, one from 0 to 1, the other from 1 to 33, I get a better result in home, 18.7499999293, but still a rather odd result in CAS of a choice of 40 or 18.7499843203.
RE: Improper integral - Onkel Otto - 06-11-2014 06:20 PM
Hmmm, using (x-1)^(-1/5) works fine in Home as well in CAS.
Buggy n-th root function ?
RE: Improper integral - ndzied1 - 06-11-2014 06:42 PM
I think it's freaking out because for the region between 0 and 1 the radical is imaginary.
RE: Improper integral - ndzied1 - 06-11-2014 06:50 PM
Thinking this is the actual problem... Am I right?
$$\Large\int_{0}^{33} \frac{1}{\sqrt[5]{x-1}} dx$$
RE: Improper integral - Onkel Otto - 06-11-2014 06:50 PM
Even integrating from 2 to 33 shows the same error.
[attachment=788]
RE: Improper integral - ndzied1 - 06-11-2014 06:56 PM
Wolfram Alpha has...
[attachment=787]
RE: Improper integral - HP67 - 06-11-2014 07:01 PM
The 50g says (21.01127123, -.734731565365) if my understanding matches ndzied1's. Which looks pretty close to Wolfram.
Why does the op say it should be 75/4?
RE: Improper integral - CR Haeger - 06-11-2014 07:15 PM
(06-11-2014 06:20 PM)Onkel Otto Wrote: Hmmm, using (x-1)^(-1/5) works fine in Home as well in CAS.
Buggy n-th root function ?
You may be right...
[attachment=789]
RE: Improper integral - HP67 - 06-11-2014 07:16 PM
But not as buggy as the TI N-Spire?
RE: Improper integral - Mark Hardman - 06-11-2014 07:22 PM
(06-11-2014 07:01 PM)HP67 Wrote: The 50g says (21.01127123, -.734731565365) if my understanding matches ndzied1's. Which looks pretty close to Wolfram.
Why does the op say it should be 75/4?
The asymptote is at x=1, I'm not sure why the OP thinks there would be a real solution in the interval 0..1.
[attachment=790]
For a reasonable endpoint, the improper integral (1..33) we get a solution of exactly 20.
[attachment=791]
This requires we use fractional powers in CAS rather than nthroot. I thought those issues had been resolved in the latest release. I guess not.
RE: Improper integral - Onkel Otto - 06-11-2014 08:21 PM
(06-11-2014 07:16 PM)HP67 Wrote: But not as buggy as the TI N-Spire?
No problems with Ti Nspire in this case :-)
RE: Improper integral - Mark Hardman - 06-11-2014 09:13 PM
(06-11-2014 06:01 PM)lrdheat Wrote: The TI NSpire immediately produces 75/4.
(06-11-2014 08:21 PM)Onkel Otto Wrote:(06-11-2014 07:16 PM)HP67 Wrote: But not as buggy as the TI N-Spire?
No problems with Ti Nspire in this case :-)
Except that the result should be 21.0113 - 0.734732i.
RE: Improper integral - Helge Gabert - 06-11-2014 09:55 PM
I only get the correct, complex result if , in CAS, I integrate separately from 0. to 1. and then from 1. to 33. (note the real upper and lower limits; the integer limits 0 and 33 return 75/4).
RE: Improper integral - Onkel Otto - 06-11-2014 09:58 PM
(06-11-2014 09:13 PM)Mark Hardman Wrote:(06-11-2014 06:01 PM)lrdheat Wrote: The TI NSpire immediately produces 75/4.
(06-11-2014 08:21 PM)Onkel Otto Wrote: No problems with Ti Nspire in this case :-)
Except that the result should be 21.0113 - 0.734732i.
That is what you get using the Nspire - even in exact notation !
[attachment=793]
RE: Improper integral - Mark Hardman - 06-11-2014 10:26 PM
(06-11-2014 09:58 PM)Onkel Otto Wrote: That is exactly what you get using the Nspire !
Lacking a TI NSpire, I have to trust the OP's claim the it gives a result of 75/4. I'm curious why his result is different from yours. Some CAS setting that he or she missed?
Damn, I just gave myself justification for buying one and have already started an eBay search.
I need professional help.
RE: Improper integral - Onkel Otto - 06-11-2014 10:46 PM
It simply depends on your Real/Complex setting :
[attachment=794]
Like using the Prime with (x-1)^(-1/5) you will receive in Real-Mode :
[attachment=795]
> I need professional help.
That's GAS (Gear Acquisition Syndrome) ! ... I do know, what I'm talking about :-).
RE: Improper integral - rprosperi - 06-11-2014 11:09 PM
(06-11-2014 10:26 PM)Mark Hardman Wrote:(06-11-2014 09:58 PM)Onkel Otto Wrote: That is exactly what you get using the Nspire !
Lacking a TI NSpire, I have to trust the OP's claim the it gives a result of 75/4. I'm curious why his result is different from yours. Some CAS setting that he or she missed?
Damn, I just gave myself justification for buying one and have already started an eBay search.
I need professional help.
You can ask for almost ANY kind of help here. Except that kind. No one here is able to grasp the real problem, hence solutions evade us...
RE: Improper integral - Mark Hardman - 06-12-2014 01:45 AM
(06-11-2014 10:46 PM)Onkel Otto Wrote: It simply depends on your Real/Complex setting :
I'm still trying to wrap my mind around how we arrive at 75/4 for the "real" result.
Graphing the real and imaginary portions of the function reinforces the need to integrate over two intervals: 0..1 and 1..33.
[attachment=797]
As posted above, the interval between 1 and 33 gives us an exact real answer of 20. The interval between 0 and 1 gives us an approximate imaginary answer of 1.01127 - 0.734732i. The magnitude of this imaginary number is exactly 5/4.
[attachment=798]
The question remaining in my mind is: Why is the magnitude of the integration between 0 and 1 treated as a negative value? -(5/4)+20=75/4.
(06-11-2014 10:46 PM)Onkel Otto Wrote: > I need professional help.
That's GAS (Gear Acquisition Syndrome) ! ... I do know, what I'm talking about :-).
If I tell my wife that I've got GAS, she's going to reply, "So, what else is new?"
Maybe I have CAS (CAS Calculator Acquisition Syndrome).
RE: Improper integral - jte - 06-12-2014 06:47 AM
(06-12-2014 01:45 AM)Mark Hardman Wrote: I'm still trying to wrap my mind around how we arrive at 75/4 for the "real" result.
Perhaps the real arithmetic nth root function is being used.
[attachment=805]
[attachment=806]