## Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning

# Chapter 5 - Section 5.4 - Indefinite Integrals and the Net Change Theorem - 5.4 Exercises - Page 410: 56

#### Answer

$\int_{3}^{5}f(x)~dx~~$ represents the difference in altitude from mile 3 to mile 5 on the trail.

#### Work Step by Step

We can state the Net Change Theorem as follows: The integral of a rate of change is the net change: $\int_{a}^{b}F'(x)~dx = F(b)- F(a)$ $f(x)~~$ is the slope of the trail at a distance of $x$ miles from the start of the trail. Therefore, $~~\int_{3}^{5}f(x)~dx~~$ represents the difference in altitude from mile 3 to mile 5 on the trail.

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