Answer
Please see the work below.
Work Step by Step
We know that the potential energy is:
$U=-\int Fdx$
$\implies U=-\int (ax^2+b)dx$
$U=-(\frac{a}{3})x^3-bx$
Essential University Physics: Volume 1 (4th Edition)
by Wolfson, Richard
Published by
Pearson
ISBN 10:
0-134-98855-8
ISBN 13:
978-0-13498-855-9
Chapter 7 - Exercises and Problems - Page 131: 39
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