Hi to all 1. The problem statement, all variables and given/known data ∫∫∫∇ψdv = ∫∫ψ ds over R over S R is the region closed by a surface S here dv and ψ are given as scalars and ds is given as a vector quantitiy. and questions asks for establishing the gradient theorem by appliying the divergence theorem to each component 2. Relevant equations Divergence theorem ∫∫∫∇.Fdv=∫∫F.ds 3. The attempt at a solution i tried writing ψ as some components or some functions of F. i actually tried lots of thing like writing ds or ψ or F in open forms. but probably i do not understand what it means by "to each component" and i couldn't find the way that i should approach to the question. this homework is due tomorrow, so i would really appreciate any help. Thanks a lot.