This question is about curvilinear integration.
The first page here, it says what the geometric meaning is when the line integral is taken with this $ds$, where this $ds$ indicates the line integral is w.r.t. the arc length.
https://www.geogebra.org/m/fRHzaMnF
https://tutorial.math.lamar.edu/Classes/CalcIII/LineIntegralsPtI.aspx
So this meaning is basically the area of a curtain hanging down from the surface $F(x,y)$ to the curve $C$. I can understand this, it sounds intuitive enough.
OK... But I also read about a similar line integrals only with $dx$ and $dy$ instead of $ds$.
$$\int_C F(x,y)\ dx$$
$$\int_C F(x,y)\ dy$$
I know their definitions, they are clear to me.
But I wonder what their geometric meaning would be.
Also, I wonder if these two ($dx$ and $dy$) curvilinear or line integrals are somehow related to each other.