integral of 1/x

This is a discussion on integral of 1/x within the A Brief History of Cprogramming.com forums, part of the Community Boards category; yes this is probably a really stupid question, but 1/x doesn't have an integral right? I wrote a scripting language ...

  1. #1
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    integral of 1/x

    yes this is probably a really stupid question, but 1/x doesn't have an integral right?

    I wrote a scripting language to graph the areas under the curve (using a numerical approximation algorithm) and on any interval with -x and x (the absolute value of x is the same) I always get an area under the curve of zero, which is what it *seems* like it should be if you consider negative area (then they just cancel), but I can't exactly prove it.

    Also, I'm not in college, so if you DO have some fancy proof I probably wont' understand it anyway because i suck

    EDIT:
    the only thing I can think of is to say that the functions are changing at the same rate when they are the same distance from zero, and that might satisfy that they are approaching the 'same infinity' (i.e i guess you cannot prove that the tangent of x from 0 to PI is approaching the 'same infinity' at pi/2, my math teacher said that one could 'approach infinity before the other' in which case the area is either positive or negative infinity but not zero).
    Last edited by Silvercord; 03-14-2004 at 01:14 PM.

  2. #2
    Registered User axon's Avatar
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    well I wont prove it for you, but the integral of 1/x is ln(|x|)

    this .pdf might be handy: http://www.riverdeep.net/math/tangib...estig/fi47.pdf

    some entropy with that sink? entropysink.com

    there are two cardinal sins from which all others spring: Impatience and Laziness. - franz kafka

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    hmm, as soon as I read that I remembered that the derivative of ln(x) is equal to 1/x but I've never read a proof.

    That looks like a good link. I'm just thinking right now.

    Thanks

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    wait, something else I want to know, what is ln(x) limited by as x approaches infinity? I don't know if I'm already supposed to know this or what.

    EDIT:
    I guess it's limited by infinity?! That's weird because it's getting slower and slower, but isn't limited
    Last edited by Silvercord; 03-14-2004 at 02:06 PM.

  5. #5
    Registered User axon's Avatar
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    right limit of ln( x ) as x approaches infinity is infinity

    some entropy with that sink? entropysink.com

    there are two cardinal sins from which all others spring: Impatience and Laziness. - franz kafka

  6. #6
    Registered User axon's Avatar
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    and lim x->0+ of ln(x) = -∞

    edit:: thats why the range of of ln(x) is (-∞, ∞)

    some entropy with that sink? entropysink.com

    there are two cardinal sins from which all others spring: Impatience and Laziness. - franz kafka

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    According to integrals.wolfram.com, the integral of 1/x is Log[X]

  8. #8
    Registered User axon's Avatar
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    same thing

    some entropy with that sink? entropysink.com

    there are two cardinal sins from which all others spring: Impatience and Laziness. - franz kafka

  9. #9
    30 Helens Agree neandrake's Avatar
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    blah and meh
    Last edited by neandrake; 03-14-2004 at 08:36 PM.
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  10. #10
    Registered User axon's Avatar
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    Originally posted by neandrake
    blah and meh
    thanks a lot, captain obvious

    some entropy with that sink? entropysink.com

    there are two cardinal sins from which all others spring: Impatience and Laziness. - franz kafka

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    Originally posted by bludstayne
    According to integrals.wolfram.com, the integral of 1/x is Log[X]
    according to my studies the integral of 1/x is ln(x)

    not log(x)

  12. #12
    Mayor of Awesometown Govtcheez's Avatar
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    Originally posted by axon
    same thing
    Are you sure? log and ln have different bases, unless he's got a weird math book.

  13. #13
    & the hat of GPL slaying Thantos's Avatar
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    Are you sure? log and ln have different bases, unless he's got a weird math boo
    Quite a few of the math papers i've read define Log to be LN. If they want log10 they actually write log10.
    Not sure of the reasonning but I've confirmed with several of the math professors that it is a common practice.

  14. #14
    'AlHamdulillah
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    . If they want log10 they actually write log10.
    Yeah, I have seen this quite a bit also. I believe it has to deal witht the fact that LN is the most commonly used log, as all other logs can be derived from it.

  15. #15
    Registered User axon's Avatar
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    >> I believe it has to deal witht the fact that LN is the most commonly used log, as all other logs can be derived from it.

    I think you hit the problem right on the head! since log could be of any base (mainly 2 or 10), we don't use it....but since ln is always of base e it could be use to calculate every logarithmic table.

    some entropy with that sink? entropysink.com

    there are two cardinal sins from which all others spring: Impatience and Laziness. - franz kafka

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