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## Homework Statement

Directly compute the flux integral [tex]\int\int(G*n dS)[/tex] where D is the part of the plane x+y+z=1 in the first octant, oriented upwards.

G = -y-z-x

My attempt at solution:

normal vector, normalized, is [tex]1/sqrt(3) * (1,1,1)[/tex] and since z=1-y-x, the integral simplifies to

[tex]1/sqrt(3)*\int\int(-1 dS)[/tex]

How do I evaluate this, without parametrization of the plane?