Let γ be a path given parametrically by σ(t). Let s denote arc length from the initial point. Then integral_γ f(s) d s | = | integral_a^b f(σ(t)) left bracketing bar σ'(t) right bracketing bar d t | = | integral_a^b f(x(t), y(t), z(t)) left bracketing bar σ'(t) right bracketing bar d t, where γ:{σ(t):a<=t<=b}.

contour integral | integral | line integral | path