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Consider ## I=\int_S \vec{v} \cdot d \vec{S}=\int_S \vec{v} \cdot \hat{n} dS##, where S is a surface that is intersected once by an line parallel to the x-axis. Show that [tex] dS=\frac{|\nabla f|}{\partial f/ \partial x}dy \ dx[/tex], and that therefore, [tex]I=\int_S \vec{v} \cdot \frac{\nabla f}{\partial f/ \partial x} dy \ dz[/tex]

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