F = x 2+y 2-z，f' = 2x，f' = 2y，f' =- 1，

The normal vector is {2x, 2y,-1}, and the unit normal vector is

{2x/√( 1+4x^2+4y^2)、2y√( 1+4x^2+4y^2)、- 1√( 1+4x^2+4y^2)}。

(2) Take the upper part of the supplementary plane ∑ 1: z = 2, x 2+y 2 ≤ 2.

I = ∫∫ = ∫∫ - ∫∫，

The former uses Gaussian formula, and the latter z=2 and dz=0, so.

I =∫∫∫[8(y- 1)+8y+ 1]dxdydz-∫∫2(8y+ 1)dxdy

= ∫dt ∫( 16rsint-7)rdr ∫dz

- ∫dt ∫( 16rsint+2)rdr

=∫dt ∫( 16rsint-7)r( 1-r^2)dr

- ∫dt ∫( 16rsint+2)rdr

=∫dt ∫[ 16(r^2-r^4)sint-7(r-r^3)]dr

- ∫dt ∫( 16r^2sint+2r)dr

=∫(-32√2/ 15)sindt-∫[(32√2/3)Sint+2]dt

= ∫[(-2√2/5)sint-2]dt

= [(2√2/5)cost-2t] = -4π