Flux through the Surface of the Plane

[waters]

Homework Statement

Find the upward flux of F = <x + z, y + z, 5 - x - y>, through the surface of the plane 4x + 2y + z = 8 in the first octant.

Homework Equations

∫∫(-P(∂f/∂x) - Q(∂f/∂y) + R)dA
where the vector F(x,y) = <P, Q, R>, dA = dxdy
and where z = f(x,y) <-- f(x,y) is the function that undergoes partial differentiaion

The Attempt at a Solution

F(f(x,y)) = <8 - 3x - 2y, 8 - 4x - y, 5 - x - y>
∂z/∂x = -4, ∂z/∂y = -2
∫∫(53-21x-11y)dxdy evaluated from x = 0 to x = 2 and y = 0 to y = 4 (shadow on the xy plane of the function 4x + 2y + z = 8)

My final answer is 80. The answer is 292/3. What am I doing wrong?

 

[waters]

Never mind. The mistake I made was integrate from y = 0 to y = 4 when it should have been from y = 0 to y = -2x + 4.