Answer
$\dfrac{43}{2}$
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: $F(x,y)=(x, y)$
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:
$\phi(x,y)=\dfrac{x^2+y^2}{2}$
Therefore, the integral can be expressed as:
$\int_C F \ dr=\phi(3, 6) -\phi(1, 1) \\=\dfrac{(3)^2+(6)^2}{2}-\dfrac{(1)^2+(1)^2}{2}\\ =\dfrac{45}{2}-1\\=\dfrac{43}{2}$
