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Homework Help: Integral 5

  1. Jan 8, 2012 #1
    1. The problem statement, all variables and given/known data

    Evalute the surface integral

    2. Relevant 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

    3. The attempt at a solution

    [itex] \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[/itex]

    Is this correct so far...if so have I to substitute for z and put in above integral. Looks like a difficult integral......?
  2. jcsd
  3. Jan 9, 2012 #2
    Something like

    [itex]\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[/itex]

    [itex]\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 [/itex].?

    Posted at this link also. Will notify both forums of any responses. Thanks
    Last edited: Jan 9, 2012
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