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Suppose [tex] D \subset \Re^3 [/tex] is a bounded, smooth domain with boundary [tex] \partial D [/tex] having outer unit normal [tex] n = (n_1, n_2, n_3) [/tex]. Suppose [tex] f: \Re^3 \rightarrow \Re [/tex] is a given smooth function. Use the divergence theorem to prove that
[tex] \int_{D} f_{y}(x, y, z)dxdydz = \int_{\partial D} f(x, y, z)n_2(x, y, z)dS[/tex]
I think I see how they might be equal but I don't know where to start as far as proving it.
[tex] \int_{D} f_{y}(x, y, z)dxdydz = \int_{\partial D} f(x, y, z)n_2(x, y, z)dS[/tex]
I think I see how they might be equal but I don't know where to start as far as proving it.