∫ | y dx
| = | ∫ | y(p) d(x(p)) |

By parametric curves

Note that two curves may have a finite number of intersections, but not intersect finitely!

A function is of **bounded variation** if it can be expressed as the sum of a monotonically increasing function and a monotonically decreasing function.

Consider two closed sensible curves that intersect finitely.
Let {<p_{i}, q_{i}>} be the set of parameter value pairs where they intersect in some irrevelant order.
I claim that the intergral over the plane of the product of their winding numbers (area of their intersection, if they are simple), is wn_{q}(<x_{p}(0), y_{p}(0)>)