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Trig function appears awkward to integrate 
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#1
Feb1713, 07:07 AM

P: 2

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 √ (sin^{2}θ + k cos^{2}θ) 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
Feb1713, 07:32 AM

P: 756

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


#3
Feb1713, 08:56 AM

P: 2

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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