1. The problem statement, all variables and given/known data Derive ∫(dr/dθ)^2 + R^2 )^0.5 dθ 2. Relevant equations x = Rcosθ y = Rsinθ 3. The attempt at a solution Arc length is the change in rise over run, which can be found using Pythagorean's Theorem. Rise is dy/dθ while run is dx/dθ. The arc length is [(dy/dθ)^2 + (dx/dθ)^2 ]^1/2 dx/dθ = (cosθ -Rsinθ) dy/dθ = (sinθ + Rcosθ) dx/dθ ^2 + dy/dθ ^2 = (cos - Rsinθ)^2 + cos^2θ - 2Rsinθcosθ + R^2sin^2θ + sin^2θ + 2Rsinθcosθ + R^2cos^θ This simplifies to [R^2(cos^2θ + sin^2θ) + sin^2 θ+cos^2θ]^2/4 Which leaves ∫√R^2 + 1 dθ But that is not the right formula!