Answer
The vector field $\overrightarrow{F}$ is not conservative.
Work Step by Step
The vector field $F(x,y)=ai+bj$ is known as conservative field throughout the domain $D$, when we have
$\dfrac{\partial a}{\partial y}=\dfrac{\partial b}{\partial x}$
$a$ and $b$ represents the first-order partial derivatives on the domain $D$.
Since, the work integral $\int_C \overrightarrow{F} \cdot \overrightarrow{dr}$ is not dependent on the path when $\int_C \overrightarrow{F} \cdot \overrightarrow{dr}=0$ for every closed curve $C$.
This shows that the work done is line integral of force.
Here, we have the work done $\overrightarrow{F}$ along two different paths $C_1$ and $C_2$ connects the two points are different.This means that the line integral of $\overrightarrow{F}$ is not path independent.
Hence, the vector field $\overrightarrow{F}$ is not conservative.
