Calculus 8th Edition

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

Chapter 5 - Applications of Integration - 5.4 Work - 5.4 Exercises - Page 387: 5

Answer

$180$ $J$

Work Step by Step

The work is calculated with the formula: $W$ = $\int_a^b{F(x)}dx$ The force function is given by $F(x)$ (in newtons) and the work (in joules) is the area under the curve, given by $$\begin{align*} \int_0^8{F(x)}dx& = \int_0^4{F(x)}dx + \int_4^8{F(x)}dx \\ &= \frac{1}{2}(4)(30)+(4)(30)\\ & = 180 J \end{align*}$$
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