Improper integral

06112014, 06:01 PM
Post: #1




Improper integral
Just got an odd result for the improper integral evaluated from 0 to 33 of 1/(5th root of x1). 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. 

06112014, 06:11 PM
Post: #2




RE: Improper integral
...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.


06112014, 06:20 PM
(This post was last modified: 06112014 07:03 PM by Onkel Otto.)
Post: #3




RE: Improper integral
Hmmm, using (x1)^(1/5) works fine in Home as well in CAS.
Buggy nth root function ? 

06112014, 06:42 PM
Post: #4




RE: Improper integral
I think it's freaking out because for the region between 0 and 1 the radical is imaginary.


06112014, 06:50 PM
Post: #5




RE: Improper integral
Thinking this is the actual problem... Am I right?
$$\Large\int_{0}^{33} \frac{1}{\sqrt[5]{x1}} dx$$ 

06112014, 06:50 PM
(This post was last modified: 06112014 07:02 PM by Onkel Otto.)
Post: #6




RE: Improper integral  
06112014, 06:56 PM
Post: #7




RE: Improper integral  
06112014, 07:01 PM
(This post was last modified: 06112014 07:03 PM by HP67.)
Post: #8




RE: Improper integral
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? It ain't OVER 'till it's 2 PICK 

06112014, 07:15 PM
Post: #9




RE: Improper integral  
06112014, 07:16 PM
Post: #10




RE: Improper integral
But not as buggy as the TI NSpire?
It ain't OVER 'till it's 2 PICK 

06112014, 07:22 PM
(This post was last modified: 06112014 07:28 PM by Mark Hardman.)
Post: #11




RE: Improper integral
(06112014 07:01 PM)HP67 Wrote: The 50g says (21.01127123, .734731565365) if my understanding matches ndzied1's. Which looks pretty close to Wolfram. 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. For a reasonable endpoint, the improper integral (1..33) we get a solution of exactly 20. 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. Ceci n'est pas une signature. 

06112014, 08:21 PM
Post: #12




RE: Improper integral  
06112014, 09:13 PM
Post: #13




RE: Improper integral
(06112014 06:01 PM)lrdheat Wrote: The TI NSpire immediately produces 75/4. (06112014 08:21 PM)Onkel Otto Wrote:(06112014 07:16 PM)HP67 Wrote: But not as buggy as the TI NSpire? Except that the result should be 21.0113  0.734732i. Ceci n'est pas une signature. 

06112014, 09:55 PM
Post: #14




RE: Improper integral
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).


06112014, 09:58 PM
(This post was last modified: 06112014 10:23 PM by Onkel Otto.)
Post: #15




RE: Improper integral
(06112014 09:13 PM)Mark Hardman Wrote:(06112014 06:01 PM)lrdheat Wrote: The TI NSpire immediately produces 75/4. That is what you get using the Nspire  even in exact notation ! 

06112014, 10:26 PM
Post: #16




RE: Improper integral
(06112014 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. Ceci n'est pas une signature. 

06112014, 10:46 PM
(This post was last modified: 06112014 10:55 PM by Onkel Otto.)
Post: #17




RE: Improper integral  
06112014, 11:09 PM
Post: #18




RE: Improper integral
(06112014 10:26 PM)Mark Hardman Wrote:(06112014 09:58 PM)Onkel Otto Wrote: That is exactly what you get using the Nspire ! 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... Bob Prosperi 

06122014, 01:45 AM
(This post was last modified: 06122014 01:46 AM by Mark Hardman.)
Post: #19




RE: Improper integral
(06112014 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. 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. 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. (06112014 10:46 PM)Onkel Otto Wrote: > I need professional help. 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). Ceci n'est pas une signature. 

06122014, 06:47 AM
Post: #20




RE: Improper integral  
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