Answer
$$f(x)=\frac{1}{4}(x^6-81x^2) .$$
Work Step by Step
We have
$$f(x)=\int_{3\sqrt x}^{x^{3/2}} t^3dt=\frac{1}{4} t^4|_{3\sqrt x}^{x^{3/2}}\\
= \frac{1}{4}(x^6-81x^2) .
$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 5 - The Integral - 5.5 The Fundamental Theorem of Calculus, Part II - Exercises - Page 262: 15
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