Chapter 5.4, Problem 56E

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

Chapter
Section

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

# If f(x) is the slope of a trail at a distance of x miles from the start of the trail, what does ∫ 3 5 f ( x )   d x represent?

To determine

To represent: the integral function 35f(x)dx.

Explanation

Given information:

The slope of the trail is f(x).

The integral function is âˆ«35f(x)dx (1)

The distance of the trail denoted as x in miles.

Calculation:

Take change of elevation as E(x) and rate of change of elevation as E'(x).

The slope of the trail f(x) represents the rate of change of elevation E'(x). Hence, f(x)=E'(x).

The net change theorem is shown below:

âˆ«abF'(x)dx=F(b)âˆ’F(a)

Here, the rate of change of [y=F(x)] with respect to x is F'(x)

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