- #1
DWill
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Homework Statement
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.
Homework Equations
Flux = Double integral of F dot n d(sigma),
where d(sigma) = |(r_u x r_v)| du dv
x = cross product
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!