If instead the force is variable over a three-dimensional curve C, then the work is expressed in terms of the line integral: W = ∫ ∫ C F ⋅ ⋅ d r = ∫ ∫ Δ Δ t F ⋅ ⋅ d r d t d t = ∫ ∫ Δ Δ t F ⋅ ⋅ v d t .