4) Test the divergence theorem for the vector function \(\mathbf{v} = (xy)\hat{\mathbf{i}} + (2yz)\hat{\mathbf{j}} + (3zx)\hat{\mathbf{k}}\) using a cube with sides of length 2 with the starting corner at the origin (see figure to the right)
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Mathematically, this is expressed as: \[ \iint_{S} \vec{v} \cdot d\vec{S} = \iiint_{V} (\nabla \cdot \vec{v}) dV \] where \(\nabla \cdot \vec{v}\) is the divergence of \(\vec{v}\). Show more…
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