What does the absolute value sign mean when used around the differential part of an integral?

The Wikipedia entry on Radon transform shows an equation like the following: $$\int_L f(\mathbf{x})|\mathbf{dx}|.$$ What does absolute value around $$|\mathbf{dx}|$$ mean in an integral?

I understand that for the Radon transform we want to integrate the function along the line $$L$$, but I don't understand the notation in the equation I listed above.

• Their link to line integral takes you right to its definition. How would you calculate the length of the curve $L$? Commented Sep 15, 2023 at 16:47
• @KurtG. I think the |dx| can be (at least loosely) interpreted as a small length along the curve L. It's not clear to me why the absolute value signs are needed. Commented Sep 15, 2023 at 17:00
• There is no looseness whatsoever in the definition for which Wikipedia and I provided a link. A good reason for the absolute value signs is that there is another type of line integral that integrates a vector along a curve ("work done"). Please google that and get familiar with it. In short: its proper notation is $\int_L\mathbf{F}\cdot d\mathbf{x}\,.$ Commented Sep 15, 2023 at 17:05
• For one thing, $|dz|$ is the natural notation in complex analysis when one wants to distinguish it from the regular $dz$ line integrals. Commented Sep 15, 2023 at 18:25
• @KurtG. I think I understand the line integral you described for "work done," but I still don't understand why the absolute value is used in Radon transform. Commented Sep 16, 2023 at 1:01