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Thread: integrating a hyperbola

  1. #1 integrating a hyperbola 
    Forum Junior whizkid's Avatar
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    I have done this integration at Wolfram:
    http://www.wolframalpha.com/input/?i...rom+0+to+995++
    it gives a result but says computation time exceeded
    If you have access to a good math program, can you check if the rsult is correct?
    Thanks


    Last edited by whizkid; July 19th, 2014 at 02:29 AM.
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  3. #2  
    Forum Radioactive Isotope MagiMaster's Avatar
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    Mathematica gives the same answer (unsurprisingly). The "time limit exceeded" just means it ran out of time to do all the other things Alpha will try and do with your expression. If it ran out of time on the main result (which certainly can happen), it wouldn't give you one at all.


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  4. #3  
    Forum Junior whizkid's Avatar
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    Thanks Magimaster,
    since you are an expert, can you explain what is (if any) the practical rule to find quicly the result.
    To simplify matters I have changed the parameters:
    integrate y= sin(tan^-1(5/x))* 50000/ (x^2+25) from 0 to 1 - Wolfram|Alpha

    I tried to deduce it from the indefinite integral, but did not succeed:

    from 0 to 1 = 5000 sqrt(2/13)
    from 0 to 2 = 20000/sqrt29
    from 0 to 5 = 5000 sqrt2
    from 0 to 10 = 4000 sqrt5
    from 0 to 1000 = 2 000 000/sqrt 40 001

    why sometimes the sqrt is above and sometimes is below?
    Thanks for your help
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  5. #4  
    Forum Radioactive Isotope MagiMaster's Avatar
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    You should probably put the square root around the whole thing ( and ).

    When you say quickly find the result, do you mean "quickly find the definite integral given the indefinite integral," or "quickly find the indefinite integral," or something else? If it's the first, then call the indefinite integral . Then the definite integral . If it's the second, there's no quick way of working out integrals.
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  6. #5  
    Moderator Moderator Markus Hanke's Avatar
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    Works perfectly fine on my iMac, both in WolframAlpha and in MAPLE. This ( rather complicated ) definite integral evaluates to 10768.4
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  7. #6  
    Forum Junior whizkid's Avatar
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    Quote Originally Posted by Markus Hanke View Post
    Works perfectly fine on my iMac, both in WolframAlpha and in MAPLE. This ( rather complicated ) definite integral evaluates to 10768.4
    It is not so complicated after all Markus, it boils down to k sin^3
    if x and 4.64.. are the legs of a triangle
    Last edited by whizkid; July 20th, 2014 at 06:00 AM.
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