Question: Let (S) be a closed surface and (V) the enclosed volume. Prove Green's first and second identities, respectively. a. (int_{S} phi abla psi cdot mathbf{n}
Let \(S\) be a closed surface and \(V\) the enclosed volume. Prove Green's first and second identities, respectively.
a. \(\int_{S} \phi abla \psi \cdot \mathbf{n} d S=\int_{V}\left(\phi abla^{2} \psi+abla \phi \cdot abla \psi\right) d V\).
b. \(\int_{S}[\phi abla \psi-\psi abla \phi] \cdot \mathbf{n} d S=\int_{V}\left(\phi abla^{2} \psi-\psi abla^{2} \phi\right) d V\).
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