Question: Let (mathbf{F}(x, y)=langle y, xangle). Prove that if (C) is any path from ((a, b)) to ((c, d)), then [ int_{C} mathbf{F} cdot d mathbf{r}=c

Let $\mathbf{F}(x, y)=\langle y, xangle$. Prove that if $C$ is any path from $(a, b)$ to $(c, d)$, then

\[
\int_{C} \mathbf{F} \cdot d \mathbf{r}=c d-a b
\]

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