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: 83

Answer

They differ by a constant, ( $G(x)-F(x)=$ Constant.)

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 $\displaystyle \int f(x)dx=F(x)+C.$ This is not one function -- it is a collection of functions, separated by some constant. These functions have the form $\quad G(x)=F(x)+C.$ In other words $G(x)-F(x)=C$, They differ by a constant, ($G(x)-F(x)=$ Constant).
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