\(\displaystyle F(x,y,z)=xze^y i -xze^y j +z k\) for the surface is partof the plane x+y+2z=2 in the first octant and orientated downwards
\(\displaystyle \displaystyle \int \int_{\sigma} F dS=\int \int_R (xze^y i -xze^y j +z k)(z_x i+ z_y j -k) dA\)
\(\displaystyle =\int \int_R (x^2z^2e^y-xyz^2e^y-z) dA
\)
\(\displaystyle =\int \int_R (x^2(\frac{2-x-y}{2})^2 e^y-xy(\frac{2-x-y}{2})^2 e^y-(\frac{2-x-y}{2})) dA
\)
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\(\displaystyle \displaystyle \int \int_{\sigma} F dS=\int \int_R (xze^y i -xze^y j +z k)(z_x i+ z_y j -k) dA\)
\(\displaystyle =\int \int_R (x^2z^2e^y-xyz^2e^y-z) dA
\)
\(\displaystyle =\int \int_R (x^2(\frac{2-x-y}{2})^2 e^y-xy(\frac{2-x-y}{2})^2 e^y-(\frac{2-x-y}{2})) dA
\)
Is this correct?
This was posted a few days ago at this link. I will notify both forums of any responses. Thanks
http://www.physicsforums.com/showthread.php?t=565951