# Work of centrifugal force cartesian coordinates

Hey I have a question about an expression in the textbook of Born. There a pendulum of variable is considered. Then it is stated that for shortening a work given by $$$$-ml \int \dot{\phi}^2 dl$$$$ is done. What I want to ask is how to express this in cartesian coordinates. I mean $$\dot{\phi} = \frac{v}{l}$$ usually, but $$l$$ is written outside of the integral. Is there a second $$l$$ in the integral?