A surface integral is a mathematical concept used to calculate the total value of a function over a surface in three-dimensional space. It extends the idea of a regular integral, which sums values along a line or area, to a two-dimensional surface. This is particularly useful in physics and engineering for analyzing quantities like mass, charge, or fluid flow across a surface. To compute a surface integral, one typically parameterizes the surface using two variables, transforming it into a double integral. The integral accounts for both the function's value and the surface's orientation, often involving concepts from vector calculus, such as the dot product and normal vector.