Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 16 - Vector Calculus - Review - Concept Check - Page 1188: 4


(a) See the explanation below. (b) See the explanation below. (c) See the explanation below

Work Step by Step

a) Suppose $F$ is a scalar function defined on the curve $C$ which is parameterized by a vector function $r(t)$ in the close interval $[m,n]$ . $\int_C F.dr=\int_Cf(r(t))ds=\int_m^nf(r(t))r'(t)dt$ b) From part (a), we have $\int_Cf(r(t))ds=\int_m^nf(r(t))r'(t)dt$. Here, $F$ defines a force field, then the line integral represents the total work done or energy required to move a object from point $n$ to $m$. c) As we are given that If $F=\lt P,Q,R \gt $ Thus,$\int_C F \cdot dr=\int_C(Pdx+Qdy+Rdz)$
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