What does it mean to take an integral: $\int y dx + xdy$
I would guess that this means that this integral over a region multiplies the infinitely small increments of $x$ ($\Delta x$) by $y$ and the infinitely small increments of $y$ ($\Delta y$) by x, but I still can't really picture what this integral does.
Is it the same as a double integral?
I'm sorry for how vague this question is, but any material you can provide me with would be appreciated.
$$\int ydx+xdy = \int <y, x>\cdot <dx, dy> = \int \textbf{F}\cdot d\textbf{r}$$
You can see that the corresponding definite integral gives work done by the force field $\textbf{F} = <y, x>$