Integral  Printable Version + HP Forums (https://archived.hpcalc.org/museumforum) + Forum: HP Museum Forums (https://archived.hpcalc.org/museumforum/forum1.html) + Forum: Old HP Forum Archives (https://archived.hpcalc.org/museumforum/forum2.html) + Thread: Integral (/thread250893.html) 
Integral  Richard Berler  09212013 Is there a way to get the integral of 1/(x1)^2/3 to evaluate as 6? I get (3*i*sqrt3 + 3)/2 on the Prime. The NSpire correctly comes with 6.
The Prime froze on a screen...reset hole worked, histories and graph was still there after reset.
Re: Integral  Richard Berler  09212013 The integral is to be evaluated from 0 to 2.
Re: Integral  peacecalc  09212013 Hello Richard, from where you got your value of the definite integral with the function 1/(x1)^(2/3) between 0 and 2? In my eyes it can't be correct because you integrate over a value x=1, where the function isn't defind. Is the function you wrote correct written?
Greetings Re: Integral  Tim Wessman  09212013 Yes, I get the prime result in wolfram alpha ... I've checked and the Nspire does spit out 6. I beleive this is a result of it being set in "real" only.
TW
Edited: 21 Sept 2013, 4:38 p.m.
Re: Integral  Matt Agajanian  09212013 Good to know. And to think, along with the Prime, I was going to add a TI NSpire for comparison. Looks like I can save my finances just buying the Prime instead of both. Thanks for the alert!
Re: Integral  Richard Berler  09212013 Dumb question...how do I do a ONSYMB ?
Re: Integral  Tim Wessman  09212013 Hold both keys down together, release. Equivalent to the ONF3 on a 50g. The onf1F6 clear memory of the 50g has a similar key sequence with onappsesc. It clears out your memory.
TW
Re: Integral  Gilles Carpentier  09212013 The TI seems wrong here. No freeze for me both with real Prime or emulator
Re: Integral  Richard Berler  09212013 Thanks for the reset instruction...this is preferable to using the reset hole in the back. Is there a way to get the principal result of 6 for the integral on the Prime?
The graphing and solve apps are really nice! (Can't stand the graphing on the NSpire and all the clutter that results on the plot when finding points of interest)
Re: Integral  Gilles Carpentier  09212013 The function is not defined on R for x<1 The NSpire result is wrong.
Edited: 21 Sept 2013, 6:38 p.m.
Re: Integral  Richard Berler  09212013 .... Re: Integral  Bunuel66  09212013 Sorry guys but could you explain me how the result can be complex.....
My 2 cents
Re: Integral  Gilles Carpentier  09212013 http://en.wikipedia.org/wiki/Cauchy_principal_value
EDIT: I tried with lim a>0'+' instead of a>0 on the Prime : same result Edited: 21 Sept 2013, 6:50 p.m.
Re: Integral  Richard Berler  09212013 ...should add up to 6.
Re: Integral  Gilles Carpentier  09212013 'f(x)=1/(x1)^2/3' is undefined on R when x<1 for example
f(0)~= 0.50.866i
Re: Integral  Gilles Carpentier  09212013 I don't understand what is (1)^(2/3) for you ? A real or a complex number ? EDIT : If I don(t allow complex (1)^(2/3) returns an error in HOME with the Prime : Error : (X<0)^(not in Z)
Edited: 21 Sept 2013, 7:12 p.m.
Re: Integral  Tim Wessman  09212013 >Is there a way to get the principal result of 6 for the integral on the Prime? I am investigating. :)
TW
Re: Integral  Richard Berler  09212013 A bit of a paradox! (1^2)^1/3 is real (1^1/3)^2 is complex. My 4th edition Heyd Study and Solutions Guide gives this example on page 274 under the topic improper integrals. They used the limits that I showed to yield 6 as the solution. The Prime doesn't plot below 1, the NSpire shows the whole plot.
Re: Integral  Richard Berler  09212013 Thanks for your interest in this!
Also, (not to sidetrack the integral question), why does the Prime generate a complex result when Complex and i are not checked in CAS setup?
Re: Integral  Gilles Carpentier  09212013 I think we spoke about this in the past and I got a headache :O ;D The problem is about rational power of negative numbers in R. Seems unclear if it is allowed or not If it is allowed, the curious thing is that you get a different result in R or C with the same argument. x in R, z in Q
x^z in R will return one thing Is this correct in a mathematical point of view?
Re: Integral  Gilles Carpentier  09212013 for what I understand,the Prime computes always in Complex domain with the CAS The CAS setup is not to change the domain from R to C but to allows complex results in variables
Edited: 21 Sept 2013, 8:17 p.m.
Re: Integral  Richard Berler  09212013 Another couple of interesting notes on this problem...in plot mode, if I enter it in as
In CAS, integral from 0 to 2 of this expression returns itself!
Re: Integral  Richard Berler  09212013 Yet another interesting note...integrating from 0 to 2 1/((x1)^2)^1/3 yields a choice of 2 answers! A message comes up saying that the exact solution disagreed with the approximate solution, and both will be displayed. When enter is pressed, I get [6 0.]
Re: Integral  Gilles Carpentier  09222013
> Tim : it seems that in some cases and in 'textbook' mode there are some confusion when you add 2 integrals. Switch to 'algebraic' to see why this 'syntax error'. By the way it works yesterday,perhaps this have to do with some settings... Works fine in algebraic
Edited: 22 Sept 2013, 4:04 a.m.
Re: Integral  Bunuel66  09222013 Sorry, I don't get the point. x^(2/3) is computed as square of cubic root of x then it is defined for x<0 as the cubic root of a negative number in R is defined. And squaring a negative is still in R.
My two cents...
Re: Integral  Nigel J Dowrick  09222013 Off the top of my head (so quite possibly I'm completely wrong) I can't think of a single cut in the complex plane that makes x^(1/3) singlevalued and real for both real x>0 and real x<0. If the real value is intended for both sections of the integral, perhaps the integral should be split into two parts to make this clear? My sympathies are with the HP Prime on this one  I think that the original integral should give a complex result, unless the contrary is clearly stated.
Nigel (UK)
Re: Integral  Richard Berler  09222013 Integral from 0 to pi of sqrt(1+cos(x)^2) generates a Taylor message, comes up zero. If I force numerical by using 1. in the integral, it comes up with the correct 3.820+ answer.
Interestingly, the NSpire comes up with 4.4418
Re: Integral  Bunuel66  09222013 Well, if we choose cubic root of x with x<0 as cubic root abs(x) which means that cubic root of 8 is 2, which is in R then there is no need of any complex value. cos(pi/3)i.sin(pi/3); 1; cos(pi/3)+i.sin(pi/3) Then any cubic root of a negative number could be a multiple of those three values. Depending of the choice the integral will be real or complex. Both results are equally right as long as the hypothesis are clear. What does the Prime if you plot cubic root of x for x in [5,5]....?
My two cents...
Re: Integral  Tim Wessman  09222013 Ok, I got the answer (and I should have remembered this yesterday). The CAS always does the calculation in the full plane (as Gilles mentioned below). In order to only evaluate a fractional power in the real plane, the "surd" command is used similar to how mathematica works. http://reference.wolfram.com/mathematica/ref/Surd.html int(1/surd(x1,3)^2,x,0,2) spits out the real only root and you get 6.
TW
Re: Integral  Tim Wessman  09222013 Yes there can be some confusion here since what actually happens integral(expr,integral(exp)... instead of integral(expr,x)+integral(expr,x). The 2D editor is not completely clear you are still in the d(x) part instead of outside it so it becomes d(x+<next_integral>). Agreed it needs to be clarified better here and give more visual cue.
TW
Re: Integral  From Hong Kong  09222013 Quote: Tim,
You're so generous to your competitor, aren't you? :P :P
Re: Integral  Richard Berler  09222013 Hi Tim,
Regardless of being in CAS or home, I get undefined or errors when I enter the integral in algebraic like you show, or attempt textbook. How are you getting it to work?
Re: Integral  Les Koller  09222013 My HP Prime Emulator and my nSpire BOTH give [3*i*sqrt(3)+3] /10. What's the problem?
