"

But, in general, there is also some ambiguity between tensors and pseudotensors (or between even and odd) when it comes to integrands.  An example in one dimension, when  and  is:

The first integral is equal to either of the other two integrals.  In the second integral the integrand transforms like a tensor (or odd tensor) density, but the integration limits are no longer from lower to higher; in a higher-dimensional example they would be no longer right-handed.  In the second integral the integrand transforms like a pseudotensor (or even tensor) density because we have kept the integration limits in proper order, −b < −a; in higher dimensions we would say that we are maintaining right-handedness.  The usual convention I've seen is to keep the coordinates right-handed and to transform the integrand as a pseudotensor density, but the other approach is equally valid.  — (talk | contribs) "