Definition. Let f be a function such that the derivative f' is continuous on the closed interval [a, b]. The arc length of f from x = a to x = b is the integral

Definition. Let x = g(y) be a function such that the derivative g' is continuous on the closed interval [c, d]. The arc length of g from y = c to y = d is the integral

Definition. Let x = h(t) and y = g(t) be parametric functions such that the derivatives h' and g' are continuous on the closed interval [r, s]. The arc length of the graph of this system of parametric functions from t = r to t = s is the integral