# Calculate the upward flux

1. Dec 9, 2008

### hils0005

1. The problem statement, all variables and given/known data
Let S be part of the plane 3x + 2y + z =9 lying in the first octant. Calculate the upward flux of vectorF(x,y,z) = x i + xy j + xz k

2. Relevant equations
z=9-3x-2y
dz/dx=-3
dz/dy=-2

F(dot)(-dz/dx i - dz/dy j + k)

3. The attempt at a solution

x i + xy j + xz k (dot) (3i +2j + k)=3x + 2xy + xz
I then substituted z: =3x + 2xy + 9x -3x^2 - 2xy

$$\int$$$$\int$$ -3x^2 + 12x dydx

0 $$\leq$$ y $$\leq$$ -4.5x/3 + 4.5
0 $$\leq$$ x $$\leq$$ 3

Any help on whether this is correct or not would be apprecitated