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An integral sign with a circle, integrating around a closed path.
Also known as: Closed integral, Loop integral, Circulation integral, Line integral over a closed curve
A circle drawn on an integral sign says the path of integration is closed — around a loop and back to the start. In complex analysis a closed contour integral can be non-zero even though the path returns to where it began, which is the fact that makes the notation worth marking.
Denotes integration around a closed curve or over a closed surface, the circle marking that the path returns to its start.
Contexts: Mathematics
Can take a non-zero value in complex analysis despite the closed path, which is the content of the residue theorem.
Contexts: Mathematics
Is drawn with an arrow on the circle in some texts to fix the direction of travel, which changes the sign of the result.
Contexts: Mathematics
A tall S-shaped stroke with a small circle drawn across its middle.
The circle is the only thing marking the path as closed.