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

Use a parametrization to find the flux across the surface in the given direction:

F = (2xy)i + (2yz)j + (2xz)k upward across the portion of the plane x + y + z = 2a that lies above the square 0 <= x <= a, 0 <= y <= a, in the xy-plane.

2. Relevant equations

Flux = Double integral of F dot n d(sigma),

where d(sigma) = |(r_u x r_v)| du dv

x = cross product

3. The attempt at a solution

I need some help coming up with a parametrization for the plane x + y + z = 2a. Since it lies in the xy-plane, I figured I can use the parametrization x = u and y = v, so I get u = 2a - v, and v = 2a - u, and z = 2a - u - v, and use order of integration du dv. However, I end up with a rather large integral with this parametrization, so I just want to make sure I'm doing this right before trying to solve it. Thanks for any suggestions!

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# Homework Help: Flux across parametrized surface

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