   Chapter 5, Problem 59RE ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

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

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Let r(t) be the rate at which the world’s oil is consumed, where f is measured in years starting at t = 0 on January 1, 2000, and r(t) is measured in barrels per year. What does ∫ 0 8 r ( t )   d t represent?

To determine

To represent: The integral function 08r(t)dt.

Explanation

Given information:

The world’s oil consumption rate is represented as r(t).

The integral function is 08r(t)dt (1)

Apply net change theorem:

abF'(x)dx=F(b)F(a)

Here, the rate of change of y=F(x) with respect to x is F'(x) and the change in y when x changes from a to b is F(b)F(a).

Assumption:

The number of barrels of oil consumed up to time t as b(t).

Calculation:

Apply net change theorem for the integral function as shown below:

Substitute b(t) for r(t) in Equation (1)

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