Improper integral

[lrdheat]

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.

[lrdheat]

...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.

[Onkel Otto]

Hmmm, using (x-1)^(-1/5) works fine in Home as well in CAS.

Buggy n-th root function ?

[ndzied1]

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

[ndzied1]

Thinking this is the actual problem... Am I right?

$$\Large\int_{0}^{33} \frac{1}{\sqrt[5]{x-1}} dx$$

[Onkel Otto]

Even integrating from 2 to 33 shows the same error.

   

[ndzied1]

Wolfram Alpha has...

   

[HP67]

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?

[CR Haeger]

(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...
   

[HP67]

But not as buggy as the TI N-Spire?

[Mark Hardman]

(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.

   

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.

[Onkel Otto]

(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 :-)

[Mark Hardman]

(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.

[Helge Gabert]

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).

[Onkel Otto]

(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 !

   

[Mark Hardman]

(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.

[Onkel Otto]

It simply depends on your Real/Complex setting :

   

Like using the Prime with (x-1)^(-1/5) you will receive in Real-Mode :

   


> I need professional help.

That's GAS (Gear Acquisition Syndrome) ! ... I do know, what I'm talking about :-).

[rprosperi]

(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...

[Mark Hardman]

(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.

   

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.

(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).

[jte]

(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.