Answer
$$ =31J$$
Work Step by Step
$$W=\int ^{x_{2}}_{x_{1}}f\left( x\right) dx=\int ^{1}_{0.5}\left( 52.8x+38.4x^{2}\right) =26.4x^{2}]^{1}_{0.5}+\dfrac {38.4x^{3}}{3}]^{1}_{0.5}$$
$$ =31J$$
Fundamentals of Physics Extended (10th Edition)
by Halliday, David; Resnick, Robert; Walker, Jearl
Published by
Wiley
ISBN 10:
1-11823-072-8
ISBN 13:
978-1-11823-072-5
Chapter 8 - Potential Energy and Conservation of Energy - Problems - Page 209: 84a
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