I don't really understand the classical notation for line integrals, namely why would you want to represent a scalar function f(x,y) as p(x,y)dx + q(x,y)dy. I also don't fully understand the geometrical interpretation of this. Though solving the problems is easy, I don't really understand what it means. The notation f(x,y)ds seems far more intuitive to me. Can anyone link me to a geometrical interpretation for the classical notation of line integrals? Thanks.