Surface Integral

Scalar Surface Integral

A scalar surface integral computes a overall value across a surface, based on instantaneous concentrations at each , e.g. overall mass from instantaneous densities

Explicit Surface

When can be expressed as

Parametric Surface

When can be expressed as

Vector Surface Integral

A vector surface integral gives you the flux over the surface. Flux is a measure of how much the vectors throughout the vector field are passing through the surface, along the normal direction.

where the normals are outwardly oriented

Explicit Surface

When can be expressed as , and

Parametric Surface

When can be expressed as