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Evaluate the surface integral:

$$\iint_S \mathbf{\vec F} \cdot d\mathbf{\vec S}$$

for the vector field

$$ \mathbf{\vec F}(x,y,z) = xze^y \mathbf{ \hat i} - xze^y \mathbf{\hat j} + z\mathbf{\hat k}$$

where $S$ is part of the plane $x + y + z = 1$ in the first octant and has a downward orientation.

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    $d\mathbf{S}$ is parallel to $\left<1,1,1\right>$ so the first two components of $\mathbf{F}$ will cancel in the integral. Therefore you need only evaluate $\int_S z\mathbf{k}\cdot\,d\mathbf{S}$.2012-08-16
  • 0
    So just the integral of z...? WHat would be the limits of the integral?2012-08-16

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