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Use the Divergence Theorem to compute the surface integral?

Use the Divergence Theorem to compute the surface integral where Q is bounded by x+y+2z=2 (first octant) and the coordi-nate planes, F=<2x-y^2, 4xz-2y, xy^3>. (Answer: 0)

The divergence for the vector field is 0, which I've calculated.

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1 Answer

div F = ∂(2x-y^2)/∂x + ∂(4xz-2y)/∂y + ∂(xy^3)/∂z = 2 - 2 = 0

By the Divergence Theorem,

The surface integral = ∫∫F⋅N dS = ∫∫∫div F dV = 0