Applied Calculus 5th Edition

Chapter Five

ACCUMULATED CHANGE: THE DEFINITE INTEGRAL

Contents

5.1 Distance and Accumulated Change

A Thought Experiment: How Far Did the Car Go?

Visualizing Distance on the Velocity Graph

Visualizing Distance on the Velocity Graph: Area Under Curve

Approximating Total Change from Rate of Change

Improving the Approximation: The Role of n and Δt

Left- and Right-Hand Sums

Writing Left- and Right-Hand Sums Using Sigma Notation

5.2 The Definite Integral

Taking the Limit to Obtain the Definite Integral

Computing a Definite Integral

Estimating a Definite Integral from a Table or Graph

Rough Estimates of a Definite Integral

5.3 The Definite Integral as Area

Relationship Between Definite Integral and Area

Area Between Two Curves

5.4 Interpretations of the Definite Integral

The Notation and Units for the Definite Integral

Bioavailability of Drugs

5.5 Total Change and the Fundamental Theorem of Calculus

Marginal Cost & Change in Total Cost

5.6 Average Value

The Definite Integral as an Average

How to Visualize the Average on a Graph

REVIEW PROBLEMS

STRENGTHEN YOUR UNDERSTANDING

PROJECTS: Carbon Dioxide in Pond Water, Flooding in the Grand Canyon

Focus on Theory

Theorems About Definite Integrals

The Second Fundamental Theorem of Calculus

Properties of the Definite Integral

5.1 DISTANCE AND ACCUMULATED CHANGE

In Chapter 2, we used the derivative to find the rate of change of a function. Here ...