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: 77

Answer

See explanation below.

Work Step by Step

If $F(x)$ is an antiderivative of $f(x)$, so $F'(x)=f(x),$ 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. More information is needed to pinpoint C, which would give a particular solution. The "indefinite" adjective highlights the fact that the antiderivative can be $ANY$ of the infinitely many functions of the form $F(x)+C.$
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