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## Homework Statement

Derive ∫(dr/dθ)^2 + R^2 )^0.5 dθ

## Homework Equations

x = Rcosθ

y = Rsinθ

## 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!