Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 17 - Line and Surface Integrals - 17.3 Conservative Vector Fields - Exercises - Page 945: 21

Answer

$\mathop \smallint \limits_C {\bf{F}}\cdot d{\bf{r}} = 6$

Work Step by Step

From Figure 17 we see that $f\left( Q \right) = 8$ and $f\left( P \right) = 2$. By Theorem 1: $\mathop \smallint \limits_C {\bf{F}}\cdot d{\bf{r}} = f\left( Q \right) - f\left( P \right) = 8 - 2 = 6$
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