Work out arc length of a curve instantly with clear inputs, formula shown and shareable results.
Arc length integrates the hypotenuse of each infinitesimal step: L = ∫√(1 + (f'(x))²) dx. The chord is always shorter, and the difference measures how much the curve bends.
Arc length
L = ∫ₐᵇ √(1 + (f'(x))²) dx
About 1.4789428, slightly more than the chord √2 ≈ 1.4142136.
The square root of a polynomial rarely has an elementary antiderivative, so quadrature is the practical route.