The flux integral of a vector field 
through an oriented surface 
is the surface integral
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where 
is the chosen unit normal vector. It measures
the net component of the vector field passing through
the surface. If 
is a piecewise smooth closed
surface forming the boundary of a bounded region 
in 
,
is continuously
differentiable on a neighborhood of the topological
closure of 
,
and 
is the outward unit
normal vector, the divergence theorem gives
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