Evaluating a Surface Integral: xze^y i -xze^y j +z k

[bugatti79]

Homework Statement

Evalute the surface integral

Homework Equations

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

The Attempt at a Solution

$\displaystyle \int \int_{\sigma} F dS=\int \int_R (xze^y i -xze^y j +z k)(z_x i+ z_y j -k) dA=\int \int_R (x^2z^2e^y-xyz^2e^y-z) dA$


Is this correct so far...if so have I to substitute for z and put in above integral. Looks like a difficult integral...?

 

[bugatti79]

Something like

$\displaystyle \int \int_{\sigma} F dS=\int \int_R (xze^y i -xze^y j +z k)(z_x i+ z_y j -k) dA=\int \int_R (x^2z^2e^y-xyz^2e^y-z) dA \implies$

$\displaystyle \int \int_{\sigma} F dS=\int \int_R (x^2(\frac{2-x-y}{2})^2 e^y-xy(\frac{2-x-y}{2})^2 e^y-(\frac{2-x-y}{2})) dA$.?

Posted at this link also. Will notify both forums of any responses. Thanks
http://www.freemathhelp.com/forum/threads/73614-surface-integral