Answer
$f(x)
= \tan( x/4) -\tan (x/2) .$
Work Step by Step
We have
$$f(x)=\int_{x/2}^{x/4}\sec^2u\ du=\tan u |_{x/2}^{x/4}\\
= \tan( x/4) -\tan (x/2) .
$$
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: 14
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