Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 13: Vector-Valued Functions and Motion in Space - Section 13.2 - Integrals of Vector Functions; Projectile Motion - Exercises 13.2 - Page 753: 1


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

Work Step by Step

Given $$ \int_{0}^{1}\left(t^{3} \mathbf{i}+7 \mathbf{j}+(t+1) \mathbf{k}\right) d t $$ Then \begin{align*} \int_{0}^{1}\left(t^{3} \mathbf{i}+7 \mathbf{j}+(t+1) \mathbf{k}\right) d t &= \frac{t}{4}\bigg|_{0}^{1} \mathbf{i}+7 t\bigg|_{0}^{1} \mathbf{j}+\left(\frac{t^{2}}{2}+t\right)\bigg|_{0}^{1} \mathbf{k}\\ &=\frac{1}{4} \mathbf{i}+7 \mathbf{j}+\frac{3}{2} \mathbf{k} \end{align*}
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