Calculus (3rd Edition)

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: 13


$f(x) = \frac{x^4}{2}-\frac{1}{2}.$

Work Step by Step

We have $$f(x)=\int_{1}^{x^2}t \ dt =\frac{1}{2}t^2 |_{1}^{x^2}\\ = \frac{x^4}{2}-\frac{1}{2}. $$
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