1. First of all, the title requires that the integrand function is rdxdy+qxdz+pdydz;

2. In addition, by remembering the three equations of dxdy = ds cosα, dxdz = ds cosβ and dydz = ds cosγ, we can get ds = dxdy/cos α = dxdz/cos β = dydz/cos γ, so we can get dxdy = (cosα dxdz)/cosβ = (cosα dydz). Therefore dxdz=- 1/z'x dxdy=- (part z divided by part x)dxdy, dydz =- 1/z' y =- (part z divided by part y) dxdy;

3. Bring these two equations into the original integrand function Rdxdy+Qdxdz+Pdydz=Rdxdy-Q (part z divided by part x)dxdy-P (part z divided by part y)dxdy=

[R-Q (part z divided by part x)-P (part z divided by part y)]dxdy.

4. Note: Since the integral parameters are X, Y, P, Q, Z in R should be changed to X, Y, P(x, Y, z)=P(x, Y, z(x, Y)), where the relationship between Z and X, Y is derived from z=z(x, Y) in the title. (Maybe you will ask why you can change it directly? It should be noted that the integration interval is still σ, which is not projected on the XOY plane. σ is derived from z=z(x, y), so σ, z=z(x, y) is constant on this surface, so the functions of p, q and r about x, y and z can be transformed into the functions of p (x, y) about x and y only.

5. The last step σ: change the integration interval σ into projection to XOY, because the integration parameter is already Dxy at this time, so when transforming σ into Dxy, you don't need to consider the projection vector, only the plus or minus of the projection area, but the question doesn't say whether the projection from σ to DXY is above or below XOY, so you need to add symbols.