free-symbols

Contour Integral Symbol

∮ denotes a contour integral in mathematics and related scientific writing.

U+222E

The symbol ∮ is commonly read as a contour integral. It’s used to represent integration along a path (a contour) in the complex plane. Copy it directly or use the provided code formats for web and software use.

Contour Integral Symbol Meaning

The ∮ symbol stands for a contour integral, typically written in complex analysis. It indicates that the integral is taken along a specified curve or path (the “contour”), rather than along a straight interval on the real line. Contour integrals are used to study functions of a complex variable and are fundamental to results like the evaluation of integrals via complex methods. In many texts, ∮ appears with integrands and a differential (for example, “dz”), emphasizing both the function being integrated and the chosen path in the complex plane.

Common uses

  • Writing complex analysis problems and solutions involving integrals over a curve
  • Labelling contour-based formulas in physics or engineering textbooks (complex methods)
  • Documenting mathematical derivations in notes, reports, and academic papers
  • Teaching materials and worksheets where integration is performed along a contour
  • Developer documentation for math typesetting and symbol references (e.g., U+222E)

Examples

∮ Contour Integral Symbol (U+222E)

  • Compute the contour integral ∮ f(z) dz around the unit circle.
  • Evaluate ∮ g(z) dz along the contour C to find the required value.
  • We take the integral ∮ h(z) dz where C is oriented counterclockwise.
  • The residue theorem applies to ∮ F(z) dz for a closed contour C.
  • In the derivation, replace the path integral with ∮ φ(z) dz over the contour.

Variations

Ready to copy

Technical codes

UnicodeU+222E
HTML Entity∮
HTML Code∮
CSS\222E

FAQ

What does ∮ mean in math?

∮ means a contour integral, i.e., an integral taken along a chosen curve (contour), commonly in complex analysis.

What is the typical context for a contour integral?

It’s most often used when working with complex functions and integrating along paths in the complex plane.

How do I copy the ∮ symbol on the web?

You can paste the character directly (∮) or use the provided HTML entity: ∮.

What is the Unicode code point for ∮?

The Unicode code point is U+222E, and the symbol’s Unicode name is CONTOUR INTEGRAL.

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