Verify the Divergence Theorem for the vector field and region.

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

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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