Is there an agreed way of expressing undirected integration in formulas?  

my idea of doing so would be to use the absolute value of the differential 


$$\int\_a^b f(x)|dx| = \int\_b^a f(x)|dx|$$


but I would like to get some feedback before actually using it.


A typical situation, in which undirected integrals are required, is integrating force along a path.



How to Express Undirected Integration
I quite like $f(x)|dx|$. Namely, $f(x)dx$ is a 1-form, whereas $f(x)|dx|$ is a density:
In differential geometry densities are used to integrate on non-orientable manifolds. They are sections of the line bundle with transition functions $|\det(d (u\circ v^{-1}))|$, from the chart $u$ to the chart $v$.
Also useful are half-densities, which form a natural pre-Hilbert space without needing a measure.


