1. The problem statement, all variables and given/known data Trying to derive the work and kinetic energy from principle ie ∫force⋅ds, for a pendulum, with θ at the vertical. 2. Relevant equations ∫force⋅dx 3. The attempt at a solution I toke the ∫mgsin(θ)⋅ds as the displacement and direction of the gravitation is opposite leading to the dot product - ∫mgsin(θ)ds, ds=Rdθ then the answer is mgR(cos(θ) - cos(θ(0)) , θ(0) is the initial, which makes sense since the path downwards leads to a positive number which corresponds to a increase in kinetic energy at the bottom. But its when you take the path where the direction of the displacement and force are the same that you get the integral - mgR(cos(θ) - cos(θ(0)). Which corresponds to opposite of the correct answer, ie loss of kinetic energy at the bottom of the pendulum... So i dont really understand how to interpret this ? I thought the answer would be the same irregardless of the direction you pick to go, you should have got an answer which was correct both ways like the first result.