what is circular integeration?could you give an example?

Answer 1

Not sure what you mean by circular integration. Do you mean the kind of integration where the integral symbol has a circle on it?

If so, those are usually called "line integrals", "path integrals", or "contour integrals".

In particular, the one with a circle means that the integration is done over a closed loop; i.e. it's a line integral that starts up and ends at the same place. This kind of thing appears a lot in Physics, where it can be shown that the net change in potential energy or voltage over a closed loop is zero (called Kirchoff's Law in Physics and Electronics).

There's a good discussion of them on Wikipedia:

http://en.wikipedia.org/wiki/Line_integral

There are also some good links at the bottom of the Wikipedia article for more investigation and examples.

Answer 2

it's a concept used in bioresearch, engineering, economics.....essentially it's a nonlinear means of analyzing multivariants within a system (including sub and supra).

Example: circular integration helps quantify viscuous and elastic decomposition within a chemical polymer application by holistically analyzing various reaction elements