>>10955793When integrating over 1-dimensional paths (curves) in higher dimensions, sometimes it is convenient to know if the path is a closed loop. In real analysis, using conservative functions, the closed loop integral is zero. In complex analysis, the values of a closed loop (contour) integral is determined by what kind of function you're integration over...there are a bunch of theorems that you can use.
You are first introduced to that symbol in calc III (multivariable calculus).
Example:
consider the function
.
And parameterized x and y like:
.
Notice for 0 < t < 2*pi, the parameterizition traces a circle of radius R.
The integral,
can also be written like:
because the integral is a closed loop, and is generally zero for that type of function.
