Given the vector field $F(x,y)=\left( \dfrac{y}{x^2 + 4y^2}, \dfrac{-x}{x^2 + 4y^2}+z, y\right)$
Let's consider the points $A=(2,1,1) \ B=(1,1,0) \ C=(0,1,0)$ and $D=(0,1,1)$
Calculate the following line integrals
$1)$ $$\int_{AD} \vec{F}d \vec{r}$$
$2)$ $$\int_{ABCDA} \vec{F}d \vec{r}$$
$3)$ $$\int_{DBCA} \vec{F}d \vec{r}$$
We denote AD to the curve that joins A with D. In the same way we denote ABCDA to the curve that joins A with B, B with C, C with D and D with A. (same with DBCA curve)
I suspect that this exercise should be done by applying properties of conservative fields. The curl of $ \vec F$ is zero but $ \vec F$ doesn't have a simply connected domain so I don't know if it is a conservative field. I tried to find a potential function that I will call $U$ such that $ \nabla U= \vec F$ but I couldn't get it so I can't conclude if $ \vec F$ is a conservative field so I don't know how to solve those line integrals.