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: 40



Work Step by Step

$W=\int_C F\cdot dr=\int_0^{1} (y^2+1)^2(2y dy)+y[e^{y^2+1}] dy$ or, $=\int_0^{1} 2y \times (y^2+1)^2+y \times [e^{y^2+1}] dy$ Suppose, $y^2+1=t; 2y dy =dt$ $=\int_1^2 t^2+\dfrac{e^t}{2} dt$ $=[\dfrac{t^3}{3}+\dfrac{e^t}{2}]_1^{2}$ $=[\dfrac{2^3}{3}+\dfrac{e^2}{2}]-[\dfrac{1^3}{3}+\dfrac{e^1}{2}]$ $=\dfrac{7}{3}+\dfrac{e^2-e}{2}$
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