Answer
$$10$$
Work Step by Step
For a vector field to be Conservative, $\dfrac{\partial f_1}{\partial y}=\dfrac{\partial f_2}{\partial x}$
We are given that the force field as: $F(x,y)=(x, 2)$
So, we can see that $\dfrac{\partial f_1}{\partial y}=0=\dfrac{\partial f_2}{\partial x}$
Next, we will find the potential function for the given vector field as:
$\phi(x,y)=\dfrac{x^2}{2}+2y$
Therefore, the integral can be expressed as:
$\int_C F \ dr=\phi(2, 4) -\phi(0, 0) \\=\dfrac{(2)^2}{2}+2(4)-0\\ =10$
