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 - Page 1086: 43


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

Work Step by Step

a) Here, we have $r'(t)=\lt 2at, 3b t^2 \gt ; r''(t) \lt 2a , 6bt \gt $ Thus, we get $F=m r''(t)=\lt 2ma, 6m bt \gt=2ma i+6mbtj; 0\leq t \leq 1$ 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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