Question: What is the Divergence Theorem? Explain how it generalizes Greens Theorem to three dimensions. THEOREM 8-Divergence Theorem Let F be a vector field whose compo-

What is the Divergence Theorem? Explain how it generalizes Green’s Theorem to three dimensions. THEOREM 8-Divergence Theorem Let F be a vector field whose compo- nents

have continuous first partial derivatives, and let S be a piecewise smooth

THEOREM 8-Divergence Theorem Let F be a vector field whose compo- nents have continuous first partial derivatives, and let S be a piecewise smooth oriented closed surface. The flux of F across S in the direction of the surface's outward unit normal field n equals the triple integral of the divergence V. F over the region D enclosed by the surface: [[ S F.ndo Outward flux = [[v.1 V.F dV. Divergence integral (2)

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