Consider a particle P that moves from a point A to a point B along a trajectory r (t), while a force F (r (t)) is applied to it. The work done by the force F is given by the integral W = ∫ ∫ r ( t 0 ) = A r ( t 1 ) = B F ⋅ ⋅ d r = ∫ ∫ t 0 t 1 F ⋅ ⋅ d r d t d t = ∫ ∫ t 0 t 1 F ⋅ ⋅ v d t , where d r is the differential element along the curve that is the trajectory of P, and v is its velocity. It is important to notice that the value of the work W depends on the trajectory r (t).