Question: Verify the Divergence Theorem for the vector field and region. (mathbf{F}(x, y, z)=langle y, x, zangle), the region (x^{2}+y^{2}+z^{2} leq 4) THEOREM 1 Divergence Theorem

Verify the Divergence Theorem for the vector field and region.

THEOREM 1 Divergence Theorem Let S be a closed surface that encloses

$\mathbf{F}(x, y, z)=\langle y, x, zangle$, the region $x^{2}+y^{2}+z^{2} \leq 4$

THEOREM 1 Divergence Theorem Let S be a closed surface that encloses a region W in R. Assume that S is piecewise smooth and is oriented by normal vectors pointing to the outside of W. If F is a vector field whose components have continuous partial derivatives in an open domain containing W, then J[ F.dS= div(F) dV 1

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The Divergence Theorem relates the flow of a vector field through a closed surface to the divergence of the field within the volume enclosed by the surface According to the theorem the surface integra... View full answer

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