Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 9: First-Order Differential Equations - Section 9.3 - Applications - Exercises 9.3 - Page 544: 9

Answer

We know from the first fundamental theorem of calculus if $h(x)$ is a continuous, real-valued function $\forall x\epsilon [a,b]$ and if $H(x)$ is given by $H(x)=\int_{a}^{x}h(y)dy$ then $H^{\prime}(x)=\frac{d}{dx}\int_{a}^{x}h(y)dy=h(x)$. Using this we can get our solution.

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