An important special case of a line integral occurs when the curve $C$ is closed, that is, when it starts and ends at the same point. In this case, we write the integral in the form \begin{equation} W = \oint\limits_C \FF\cdot d\rr \end{equation} and refer to it as the circulation of $\FF$ around $C$. Unless otherwise specified, it is assumed that the curve is oriented in the counterclockwise direction. As with all vector line integrals, reversing the orientation results in an overall minus sign.

This notation can also be used for scalar line integrals, such as finding the mass of a ring of wire, which could be written in the form \begin{equation} M = \oint\limits_C \lambda \,ds \end{equation} although in this case the orientation doesn't matter. One way to remember this difference between vector and scalar integrals is to realize that $ds=|d\rr|$, and the magnitude of a vector does not depend on its direction.