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.