University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 5 - Section 5.4 - The Fundamental Theorem of Calculus - Exercises: 45

Answer

${\sqrt {1+x^2}}$

Work Step by Step

Let's take the derivative of both sides! $\frac{dy}{dx}=\frac{d}{dx}\int_{0}^{x} {\sqrt {1+t^2}} dt$ Let's use the fundamental theorem of Calculus (substitute the limits, and multiply by their derivatives)! $\frac{dy}{dx}= {\sqrt {1+x^2}}\cdot 1-{\sqrt {1+0^2}}\cdot 0= {\sqrt {1+x^2}}$
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