University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 12 - Section 12.2 - Integrals of Vector Functions; Projectile Motion - Exercises - Page 654: 1


$\dfrac{1}{4}i+7j+\dfrac{3}{2} k$

Work Step by Step

We need to integrate the given integral as follows: $\int_0^1 [t^3i+7j +(t+1) k] dt= \dfrac{t^4}{4}i+7tj+(\frac{t^2}{t}+t) k]_0^1$ or, $\dfrac{t^4}{4}i+7tj+(\frac{t^2}{t}+t) k]_0^1=[\dfrac{1}{4}i+7(1)j+(\frac{1}{1}+1) k]]-\dfrac{0}{4}i+7(0)j+(\frac{0}{0}+0) k]]$ Thus, $[\dfrac{1}{4}i+7(1)j+(\frac{1}{1}+1) k]]-\dfrac{0}{4}i+7(0)j+(\frac{0}{0}+0) k]]=\dfrac{1}{4}i+7j+\dfrac{3}{2} k$
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