For three dimensional spaces, if ∇ ∇ Q defined on an open domain D ⊂ ⊂ R 3 is of differentiability class C 1 (equivalently Q is of C 2 ), then this integral path independence can also be proved by using the vector calculus identity ∇ ∇ × × ( ∇ ∇ Q ) = 0 and the Stokes' theorem.