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Math Help - Integrating a chain

  1. #1
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    Integrating a chain

    Hi all,

    Does anybody know how I might integrate this:

    1 / [(1-x^2)^1/2] ??

    i.e. One over the square root of (1 minus x squared). As you can tell I haven't yet learnt how you make it look all mathsy on these applets.

    Any help appreciated.

    Cheers.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by DangerousDave View Post
    Hi all,

    Does anybody know how I might integrate this:

    1 / [(1-x^2)^1/2] ??

    i.e. One over the square root of (1 minus x squared). As you can tell I haven't yet learnt how you make it look all mathsy on these applets.

    Any help appreciated.

    Cheers.
    Let x=\sin(\theta). You'll get quite a satisfying result.
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  3. #3
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    Thanks for the hint. That leaves me at integrating sec(x), right? - I've had a little scout around and that seems like rather a complex (though ultimately manageable) affair. I just wanted to check that the task is as I've pictured it (I'm perplexed because this seems like a much harder problem than any of the other problems on this paper)

    Edit: I mean sec theta
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by DangerousDave View Post
    Thanks for the hint. That leaves me at integrating sec(x), right? - I've had a little scout around and that seems like rather a complex (though ultimately manageable) affair. I just wanted to check that the task is as I've pictured it (I'm perplexed because this seems like a much harder problem than any of the other problems on this paper)

    Edit: I mean sec theta
    Close. You forgot to account for dx=\cos(\theta)\text{ }d\theta
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  5. #5
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    Duh me! So it all comes out at inverse sin of x (plus c) ?
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  6. #6
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by DangerousDave View Post
    Duh me! So it all comes out at inverse sin of x (plus c) ?
    !
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  7. #7
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    Many thanks for your help!
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