A line integral (with respect to arc length) can be interpreted geometrically as the area under $f(x,y)$ along $C$ as in the picture. You sum up the areas of all the infinitesimally small 'rectangles' formed by $f(x,y)$ and $ds$.

![enter image description here](https://i.stack.imgur.com/8LVrc.png)

What I'm wondering is how do I interpret line integrals **with respect to $x$ or $y$** geometrically?