A curve represented by x = x(t ), y = y(t ) for t₁≤ t ≤ t₂, with x(t₁) = x₁, x(t₂) = x₂, y(t₁) = y₁, y(t₂) = y₂, has length from (x₁,y₁) to (x₂,y₂) given by the integral from t₁ to t₂ of the function √((dx /dt )² + (dy/dt )²).