\oint

The symbol \oint is used to denote a contour integral, which is an integral taken over a path in the complex plane. It is commonly used in complex analysis and physics, particularly in the context of evaluating integrals around closed curves.

Examples

Contour integral of a function f(z) over a closed curve C.

\oint_C f(z) \, dz

Contour integral of 1/z over the unit circle, illustrating the residue theorem.

\oint_{|z|=1} \frac{1}{z} \, dz = 2\pi i

Line integral over a closed path \gamma in the xy-plane.

\oint_{\gamma} (x^2 + y^2) \, dx + (2xy) \, dy