VC5.31

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Using the cartesian form of Gauss Divergence theorm,we have

\iint _{S}(xdydz+ydzdx+zdxdy)=\iiint _{V}[{\frac  {\partial }{\partial x}}(x)+{\frac  {\partial }{\partial y}}(y)+{\frac  {\partial }{\partial z}}(z)]dV\,,V being teh volume enclosed by S.

=\iiint _{V}(1+1+1)dV\,

=3V\,

=3\times [{\frac  {4}{3}}\pi (2)^{3}]\,

=32\pi \,

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