7.G(u,v)=(2u+v,u-4v,3u)
u=1,v=4
T_u=[2 1 3]
T_v=[1 -4 0]
N(u,v)=3[4 1 -3]
4x+y=3z
13.G(u,v)=
(ucosv,usinv,u)
0<=u<=1,0<=v<=1
f(x,y,z)=sqrt(x^2+y^2)
Int(f.u_r)(S)(S)
sqrt(2)/5
15.y=9-z^2
0<=x<=3
0<=z<=3
f(x,y,z)=z
Int(f.u_r)(S)(S)
37sqrt(37)/4
19.x^2+y^2+z^2=4
0<=z<=4
f(x,y,z)=1/e^z
Int(f.u_r)(S)(S)
4pi(1-e^-4)

5.F=(y,z,x)
3x-4y+z=1
S:0<=x<=1
0<=y<=1
Int(F.dS)(S)
-4
7.F=[0,3,x]
x^2+y^2+z^2=9
x,y,z>=0
Int(F.dS)(S)
27/12(3pi+4)
9.F=[z,z,x]
z=9-x^2-y^2
x,y,z>=0
693/5
11.F=[y^2,2,-x]
x+z+z=1,x,y,z>=0
11/12