Identify the curve and the interval for the arc length, usually from (x=a) to (x=b) or from (t=t_1) to (t=t_2)
If the curve is given as (y=f(x)): use
(L=displaystyle int_{a}^{b}sqrt{1+left(frac{dy}{dx}right)^2},dx)
If the curve is given parametrically as (x=x(t)), (y=y(t)): use
(L=displaystyle int_{t_1}^{t_2}sqrt{left(frac{dx}{dt}right)^2+left(frac{dy}{dt}right)^2},dt)
If the curve is given in polar form (r=r(theta)): use
(L=displaystyle int_{alpha}^{beta}sqrt{r^2+left(frac{dr}{dtheta}right)^2},dtheta)
Evaluate the integral on the specified interval
If the integral has no elementary antiderivative, use numerical integration methods (e.g., Simpson’s rule)