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Trig function appears awkward to integrate

  1. Feb 17, 2013 #1
    I hope this isn't too simple for the maths forum.

    I'm trying to find the length of the locus described by the bottom of a garage door as it is raised. It's all fairly straightforward until I have to integrate a function of the form

    √ (sin2θ + k cos2θ)

    k does not depend on θ. I tried several approaches to the problem and always came back to the above function.

    In the end I integrated numerically and got my number which checks with reality. There's probably some nifty substitution but just I can't find it.
  2. jcsd
  3. Feb 17, 2013 #2
  4. Feb 17, 2013 #3
    Thank you very much indeed. That looks like the clue I need. (As you've probably gathered I'm an Engineer and not a mathematician.)
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