Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 13 - Section 13.1 - The Indefinite Integral - Exercises - Page 961: 79

Answer

Linear functions are antiderivatives of constant functions.

Work Step by Step

If $F(x)$ is an antiderivative of $f(x)$, that is $ F'(x)=f(x)$, then the indefinite integral of f is $\displaystyle \int f(x)dx=F(x)+C.$ If $ F(x)=ax+b$ (a linear function), then $ F'(x)=a$ (a constant function). So, linear functions are antiderivatives of constant functions.
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