Let $\mathbf{F}(x,y) = \langle 2, 3 \rangle$. Suppose $C$ is a curve connecting $(0,0)$ to $(1,1)$. Does the value of $\int_C \mathbf{F}\cdot d\mathbf{r}$ depend on the shape of the curve $C$? If not, find the value of the integral.
Solution
We are being asked if the value of a line integral is path independent. Recall that