Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 16 - Section 16.2 - Line Integrals - 16.2 Exercise: 17


a) positive b) negative

Work Step by Step

a) Along x=-3, the vectors of F have positive y-components so since the path goes upward, $F\cdot T$ is always positive. Therefore $\int_{C_{1}}F\cdot dr$ = $\int_{C_{1}}F\cdot T ds$ is positive. b) All nonzero field vectors along the circle with radius 3 are pointed in the clockwise direction, opposite the direction to the path. Therefore $F\cdot T$ is negative and $\int_{C_{2}}F\cdot dr$ = $\int_{C_{2}}F\cdot T ds$ is negative.
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