Answer
$\frac{25\pi}{4}.
$
Work Step by Step
As in the figure below, the area will be the area of a quarter of a circle of radius $5$, as follows
$$
\int_{0}^{5} \sqrt{25-x^2} d x= \frac{25\pi}{4}.
$$
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 - 5.2 The Definite Integral - Exercises - Page 244: 7
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