Calculus 8th Edition

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

Chapter 16 - Vector Calculus - 16.2 Line Integrals - 16.2 Exercises - Page 1126: 43


a) $2ma i+6mbtj; 0\leq t \leq 1$ b) $2ma^2+\dfrac{9mb^2}{2}$

Work Step by Step

a) $r'(t)=\lt 2at, 3b t^2 \gt ; r''(t) \lt 2a , 6bt \gt $ Since, $F=m r''(t)$ $F=\lt 2ma, 6m bt \gt$ $F=2ma i+6mbtj$ and $ 0\leq t \leq 1$ b) $W=\int_A^B F\cdot dr=\int_0^1 \lt 2ma, 6m bt \gt \cdot \lt 2at, 3bt^2 \gt dt$ $=\int_0^1 4ma^2 +18mb^2t^3 dt$ $=2m[a^2t^2+\dfrac{b^2t^4}{4}]_0^1$ $=2ma^2+\dfrac{9mb^2}{2}$
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