## Trig function appears awkward to integrate

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.
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 See at the elliptic functions. http://mathworld.wolfram.com/Ellipti...econdKind.html
 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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