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surface integral

The double integral obtained through integration of a functio f = (x, y) over a surface S whose vertical projection on the xy-plane in the region of R. The surface integral gives the volume between the surface and the xy-plane and is written
surface integral
In vector notation (see vector analysis), the surface integral is generally written
surface integral in vector notation
which is a scalar, dS being a surface element treated as the vector dx × dy and V being a vector function.

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