surface integral

American  

noun

Mathematics.

1. the limit, as the norm of the partition of a given surface into sections of area approaches zero, of the sum of the product of the areas times the value of a given function of three variables at some point on each section.

---

Etymology

Origin of surface integral

First recorded in 1870–75

Example Sentences

Thus, a surface integral is similar to a line integral but in one higher dimension.

From Textbooks • Mar. 30, 2016

Evaluate surface integral ∬SyzdS, where S is the first-octant part of plane x + y + z = λ, where λ is a positive constant.

From Textbooks • Mar. 30, 2016

We can extend the concept of a line integral to a surface integral to allow us to perform this integration.

From Textbooks • Mar. 30, 2016

Evaluate a surface integral over a more convenient surface to find the value of A.

From Textbooks • Mar. 30, 2016

It is now well known as Stokes's theorem connecting a certain surface integral with a line integral, and has many applications both in physics and in geometry.

From Lord Kelvin An account of his scientific life and work by Gray, Andrew