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Math Help - Surface area of a cycloid

  1. #1
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    Surface area of a cycloid

    Hi all...working on coming up with the surface area of a cycloid. I'll spare you the process of getting there, but what I've come up with is this integral:



    The a is a positive constant defined in the original question.

    I don't know how to solve that integral, though. I've played around with some identities in hopes of finding one that would help but I haven't come up with anything. What's the solution to this one?
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by Malaclypse View Post
    Hi all...working on coming up with the surface area of a cycloid. I'll spare you the process of getting there, but what I've come up with is this integral:



    The a is a positive constant defined in the original question.

    I don't know how to solve that integral, though. I've played around with some identities in hopes of finding one that would help but I haven't come up with anything. What's the solution to this one?
    Hint
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  3. #3
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    That pretty much did the trick, thank you!!!

    I still have one problem, though...when I work that through I end up with:


    Edit: Duhhh...nevermind. It's been a long night. It helps when you actually put your original variable back in after u-sub...
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