I'm not sure if this is the right place to put this?

Show that: curl(fu) = fcurlu+ (gradf) xu

By using this in relation to Stoke's theorum, show that for a simple closed curve C,

(Line integral) fdS= -(surface integral) (gradf) xdS

Firstly, is this a typo? I've never heard of a line integral of a function wrt to surface element?

I think Stoke's Theorum is:

(Line integral)(A.dl) = (surface integral)((curlA).dS)

I did the first part fine. I then tried to do

(surface integral) (gradf)xdS= (surface integral) (curl(fdS) - fcurldS)

I then got stuck. Please help!