# Homework Help: Integral 5

1. Jan 8, 2012

### bugatti79

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

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

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

2. Jan 9, 2012

### 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