Let (mathbf{F}(x, y)=langle x, 0angle). Prove that if (C) is any path from ((a, b)) to ((c,

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Let \(\mathbf{F}(x, y)=\langle x, 0angle\). Prove that if \(C\) is any path from \((a, b)\) to \((c, d)\), then

\[
\int_{C} \mathbf{F} \cdot d \mathbf{r}=\frac{1}{2}\left(c^{2}-a^{2}ight)
\]

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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