# surface integral

The surface integral is the double integral obtained through
integration of a function *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

In vector notation (see vector analysis), the surface integral is generally written

which is a scalar, *d***S** being a surface element treated as the vector *d***x** × *d***y** and **V** being a vector
function.