Hi guys! I hope someone here will be able to help me with this question:
f(r) is a scalar field, then use stoke's theorem (∫∫c curlF.dS=∫cF.dr) to deduce that:
∫∫s grad(f) x dS = -∫c f dr
I am stuck as to how to do this. I have tried subbing in the vector calculus identity curl(fu)=fcurl(u)+(gradf)xu (where u is a constant). Thus
∫∫s grad(f) x dS = ∫∫s curl(fu) - fcurl(u) (where dS is u)
but I am not sure whether this is right (and i then get stuck at this point too). Please help!