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#26 2006-02-15 12:36:42

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: integration trouble

not all the time. But on occasions were it happens, best to be prepared.


A logarithm is just a misspelled algorithm.

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#27 2006-02-15 14:16:42

irspow
Member
Registered: 2005-11-24
Posts: 455

Re: integration trouble

If you guys want to laugh, Mathmatica's online integrator gives;

(1/27)√(9 + 4/(x^(2/3)))(9x^(2/3) + 4)(x^(1/3)) for the integral I solved above.

  I put it into my TI-89 and it spit out an even more ridiculous answer. 

  I checked and my little (x^(2/3) + 4/9)^(3/2) produces the same values as the mess above.

  What in the world are these people at Mathmatica and Texas Instruments thinking about?

  Sorry ryos, but this seems to be a perfect example of why we might not want to use calculators if we don't have to.

  It took me ten minutes just to simplify that to;

  √((729x^2 + 972x^(4/3) + 432x^(2/3) + 64) / 729)

  I don't know what algorithyms they're using, but I think that they need to hire some more math majors.

Last edited by irspow (2006-02-15 14:51:19)

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#28 2006-02-17 12:22:24

irspow
Member
Registered: 2005-11-24
Posts: 455

Re: integration trouble

Is the Mathmatica Integrator broken or that limited?

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#29 2006-02-17 13:28:22

ryos
Member
Registered: 2005-08-04
Posts: 394

Re: integration trouble

As my Calc teacher once said, "Machines sometimes give us some interesting answers..."

Remember that computers have no intuition. I'm sure they've got their algorithms such that if a function can be integrated, they will integrate it somehow. It's doubtless not the best at selecting the proper method for every integral, and for some it probably doesn't have a "best method." But if you have the attention span of a computer, it works just fine.

Or maybe somebody taught the computer about artificial job security...

Anyway, I guess this is a case where a calculator isn't the best tool after all. Though, if you're using computers end to end, then the computer doesn't care how ugly the function you ask it to evaluate is...


El que pega primero pega dos veces.

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#30 2006-02-18 01:23:22

irspow
Member
Registered: 2005-11-24
Posts: 455

Re: integration trouble

You are correct ryos, it wouldn't really matter if this problem was to be solved by a computer.  The two answers are indeed equal.  I was thinking however about the scenario in which the result was going to be an integral (pun not intended) part of one's work.  Remembering and applying their formula would be much harder than would be necessary.  I, for one, had until now believed that such programs simplified their answers for our convenience.

  Sorry for making such a big thing of this, but I found it really interesting.  My level of "trust" in such software has diminished as a result anyway.

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#31 2006-02-18 06:40:26

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: integration trouble

at any rate, a simpler formula will be quicker to evaluate by the computer. (so we could all save a few billionths of a second)


A logarithm is just a misspelled algorithm.

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#32 2006-02-18 18:27:58

ryos
Member
Registered: 2005-08-04
Posts: 394

Re: integration trouble

irspow wrote:

You are correct ryos, it wouldn't really matter if this problem was to be solved by a computer.  The two answers are indeed equal.  I was thinking however about the scenario in which the result was going to be an integral (pun not intended) part of one's work.

And that, in a nutshell, is the difference between scientists and engineers. tongue


El que pega primero pega dos veces.

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