Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 7 - Integration - Chapter Review - Review Exercises - Page 417: 9

Answer

True

Work Step by Step

Fundamental theorem of Calculus states that for a continuous function $f$ on the interval $[a,b]$ and for any antiderivative of $f$, say $F$, $\int_a^bf(x)dx=F(b)-F(a)=F(x)|_a^b.$ $\int_a^bf(x)dx$ is the definite integral and $F(x)$ is the antiderivative of $f(x)$. Clearly, the theorem demonstrates a relationship between the both, i.e. the definite integral and an antiderivative of the function. Hence it is true.
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