z=g(x,y)

F= iF1 + j F2 + k F3

F.ds= F1. dy dz + F2 . dzdx + F3 dxdy

For integrating above F3 dxdy is Ok

But to integrate about say F2dzdx

How to find dz ?

Some one told it is - dz/dy.dy partial derivative and negative also.

How it came so?

So F2dzdx becomes F2(x,y,z(x,y)) . [-dz/dx](x,y) . dxdy