A surface integral is the summation of the values taken by a function, typically a vector, over every point in the region of a surface. If the surface integral is of a vector function, then it typically entails a dot product of the vector function with the vector normal (perpendicular) to the surface.
The most common use of a surface integral is to express the flux of a vector field F (such as an electric force) over a particular surface S.
There are three common techniques for solving surface integrals:
- projecting the surface onto a coordinate plane, and then performing a double integral over the coordinates for that plane.
- applying Stokes' Theorem
- applying the Divergence Theorem