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The divergence theorem


Let V be a simple solid region oriented with outward normals that has a piecewise-smooth boundary surface S.
\oiint, start subscript, S, end subscript, open bracket, cosine, left parenthesis, x, right parenthesis, \imath, with, hat, on top, plus, sine, left parenthesis, y, right parenthesis, \jmath, with, hat, on top, plus, tangent, left parenthesis, x, y, right parenthesis, k, with, hat, on top, close bracket, dot, d, S
Use the divergence theorem to rewrite the surface integral as a triple integral.
\iiint, start subscript, V, end subscript
d, V