(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

∫∫(-P(∂f/∂x) - Q(∂f/∂y) + R)dA

where the vectorF(x,y) = <P, Q, R>, dA = dxdy

and where z = f(x,y) <-- f(x,y) is the function that undergoes partial differentiaion

3. 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?

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# Homework Help: Flux through the Surface of the Plane

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