# Integral with circle in it.

what does that sign mean? a integral sign with a circle on it.

It usually refers to a line integral, which is the integral of a function around a closed loop in the domain of the function. Sometimes it is extended to higher dimensions, e.g. to represent an integral over a closed surface.

so this line integral is the same as a normal integral?

Originally posted by PrudensOptimus
so this line integral is the same as a normal integral?

A line integral is performed not over the entire domain of the integrand, but only over a one-dimensional subspace of the domain (a closed curve).

Tom Mattson
Staff Emeritus
Gold Member
Originally posted by Ambitwistor
A line integral is performed not over the entire domain of the integrand, but only over a one-dimensional subspace of the domain (a closed curve).

A "normal" integral need not be performed over the entire domain of the integrand, either.

Originally posted by PrudensOptimus
so this line integral is the same as a normal integral?

By "normal integral" I take you to mean "integral along the x-axis".

A line integral is a generalization of a "normal integral". Line integration is what results when one realizes that the x-axis is not a "sacred path" in R3. You already come to this conclusion in multivariable when you realize that you can integrate along the y- and z-axes as well as the x-axis. But you take this notion further in line integration when you remove the restriction that the path of integration be a straight line.

The so-called "normal integral" is a line integral. The "line" is just the x-axis. If you want the "normal" analog to the closed path integral, then you can integrate your function from a to b, and then add to it the integral of the same function from b to a.

HallsofIvy
Everywhere you see it, the symbol $\oint$ may be replaced with $\int$ with no change in meaning. The circle is only there to emphasize the fact that the path (or surface or whatever) you are integrating over is closed.