On the other hand, the definition of a surface integral also includes a triple product—the very same one! ∬ ∬ Σ Σ ( ∇ ∇ × × F ) ⋅ ⋅ d Σ Σ = ∬ ∬ D ( ∇ ∇ × × F ) ( ψ ψ ( u , v ) ) ⋅ ⋅ ∂ ∂ ψ ψ ∂ ∂ u ( u , v ) × × ∂ ∂ ψ ψ ∂ ∂ v ( u , v ) d u d v