Chapter 5.4, Problem 72E

BuyFind*arrow_forward*

8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

Shown is the graph of traffic on an Internet service provider’s T1 data line from midnight to 8:00 am. *D* is the data throughput, measured in megabits per second. Use the Midpoint Rule to estimate the total amount of data transmitted during that time period.

To determine

**To calculate:** The total amount of data transmitted during 8 hours’ time period.

Explanation

**Given information:**

Duration of data transmission is

The general expression for midpoint rule is shown below:

Apply the conditions for midpoint rule as follows:

Here, width of the subinterval is *b*, the lower limit is *a*, the number of subinterval is *n*, and the midpoint of

**Calculation:**

Find the width of the subinterval

Consider the number of subintervals as 4.

Substitute 4 for *n*, 8 hours for *b* and 0 for *a* in Equation (1).

The expression to find the total amount of data transmitted

Here, the amount of data transmitted at time

Sect-5.1 P-1ESect-5.1 P-2ESect-5.1 P-3ESect-5.1 P-4ESect-5.1 P-5ESect-5.1 P-6ESect-5.1 P-7ESect-5.1 P-8ESect-5.1 P-13ESect-5.1 P-14E

Sect-5.1 P-15ESect-5.1 P-16ESect-5.1 P-17ESect-5.1 P-18ESect-5.1 P-19ESect-5.1 P-20ESect-5.1 P-21ESect-5.1 P-22ESect-5.1 P-23ESect-5.1 P-24ESect-5.1 P-25ESect-5.1 P-26ESect-5.1 P-27ESect-5.1 P-28ESect-5.1 P-32ESect-5.2 P-1ESect-5.2 P-2ESect-5.2 P-3ESect-5.2 P-4ESect-5.2 P-5ESect-5.2 P-6ESect-5.2 P-7ESect-5.2 P-8ESect-5.2 P-9ESect-5.2 P-10ESect-5.2 P-11ESect-5.2 P-12ESect-5.2 P-14ESect-5.2 P-15ESect-5.2 P-16ESect-5.2 P-17ESect-5.2 P-18ESect-5.2 P-19ESect-5.2 P-20ESect-5.2 P-21ESect-5.2 P-22ESect-5.2 P-23ESect-5.2 P-24ESect-5.2 P-25ESect-5.2 P-26ESect-5.2 P-27ESect-5.2 P-28ESect-5.2 P-29ESect-5.2 P-30ESect-5.2 P-33ESect-5.2 P-34ESect-5.2 P-35ESect-5.2 P-36ESect-5.2 P-37ESect-5.2 P-38ESect-5.2 P-39ESect-5.2 P-40ESect-5.2 P-41ESect-5.2 P-42ESect-5.2 P-43ESect-5.2 P-44ESect-5.2 P-45ESect-5.2 P-46ESect-5.2 P-47ESect-5.2 P-48ESect-5.2 P-49ESect-5.2 P-50ESect-5.2 P-51ESect-5.2 P-52ESect-5.2 P-53ESect-5.2 P-54ESect-5.2 P-55ESect-5.2 P-56ESect-5.2 P-57ESect-5.2 P-58ESect-5.2 P-59ESect-5.2 P-60ESect-5.2 P-61ESect-5.2 P-62ESect-5.2 P-63ESect-5.2 P-64ESect-5.2 P-65ESect-5.2 P-66ESect-5.2 P-67ESect-5.2 P-68ESect-5.2 P-69ESect-5.2 P-70ESect-5.2 P-71ESect-5.2 P-72ESect-5.2 P-73ESect-5.2 P-74ESect-5.2 P-75ESect-5.3 P-1ESect-5.3 P-2ESect-5.3 P-3ESect-5.3 P-4ESect-5.3 P-5ESect-5.3 P-6ESect-5.3 P-7ESect-5.3 P-8ESect-5.3 P-9ESect-5.3 P-10ESect-5.3 P-11ESect-5.3 P-12ESect-5.3 P-13ESect-5.3 P-14ESect-5.3 P-15ESect-5.3 P-16ESect-5.3 P-17ESect-5.3 P-18ESect-5.3 P-19ESect-5.3 P-20ESect-5.3 P-21ESect-5.3 P-22ESect-5.3 P-23ESect-5.3 P-24ESect-5.3 P-25ESect-5.3 P-26ESect-5.3 P-27ESect-5.3 P-28ESect-5.3 P-29ESect-5.3 P-30ESect-5.3 P-31ESect-5.3 P-32ESect-5.3 P-33ESect-5.3 P-34ESect-5.3 P-35ESect-5.3 P-36ESect-5.3 P-37ESect-5.3 P-38ESect-5.3 P-39ESect-5.3 P-40ESect-5.3 P-41ESect-5.3 P-42ESect-5.3 P-43ESect-5.3 P-44ESect-5.3 P-45ESect-5.3 P-46ESect-5.3 P-47ESect-5.3 P-48ESect-5.3 P-49ESect-5.3 P-50ESect-5.3 P-51ESect-5.3 P-52ESect-5.3 P-53ESect-5.3 P-54ESect-5.3 P-55ESect-5.3 P-56ESect-5.3 P-57ESect-5.3 P-58ESect-5.3 P-59ESect-5.3 P-60ESect-5.3 P-61ESect-5.3 P-62ESect-5.3 P-63ESect-5.3 P-64ESect-5.3 P-65ESect-5.3 P-66ESect-5.3 P-67ESect-5.3 P-68ESect-5.3 P-69ESect-5.3 P-70ESect-5.3 P-73ESect-5.3 P-74ESect-5.3 P-75ESect-5.3 P-76ESect-5.3 P-77ESect-5.3 P-78ESect-5.3 P-79ESect-5.3 P-80ESect-5.3 P-81ESect-5.3 P-82ESect-5.3 P-83ESect-5.3 P-84ESect-5.3 P-85ESect-5.3 P-86ESect-5.4 P-1ESect-5.4 P-2ESect-5.4 P-3ESect-5.4 P-4ESect-5.4 P-5ESect-5.4 P-6ESect-5.4 P-7ESect-5.4 P-8ESect-5.4 P-9ESect-5.4 P-10ESect-5.4 P-11ESect-5.4 P-12ESect-5.4 P-13ESect-5.4 P-14ESect-5.4 P-15ESect-5.4 P-16ESect-5.4 P-17ESect-5.4 P-18ESect-5.4 P-19ESect-5.4 P-20ESect-5.4 P-21ESect-5.4 P-22ESect-5.4 P-23ESect-5.4 P-24ESect-5.4 P-25ESect-5.4 P-26ESect-5.4 P-27ESect-5.4 P-28ESect-5.4 P-29ESect-5.4 P-30ESect-5.4 P-31ESect-5.4 P-32ESect-5.4 P-33ESect-5.4 P-34ESect-5.4 P-35ESect-5.4 P-36ESect-5.4 P-37ESect-5.4 P-38ESect-5.4 P-39ESect-5.4 P-40ESect-5.4 P-41ESect-5.4 P-42ESect-5.4 P-43ESect-5.4 P-44ESect-5.4 P-45ESect-5.4 P-46ESect-5.4 P-47ESect-5.4 P-48ESect-5.4 P-49ESect-5.4 P-50ESect-5.4 P-51ESect-5.4 P-52ESect-5.4 P-53ESect-5.4 P-54ESect-5.4 P-55ESect-5.4 P-56ESect-5.4 P-57ESect-5.4 P-58ESect-5.4 P-59ESect-5.4 P-60ESect-5.4 P-61ESect-5.4 P-62ESect-5.4 P-63ESect-5.4 P-64ESect-5.4 P-65ESect-5.4 P-66ESect-5.4 P-67ESect-5.4 P-68ESect-5.4 P-69ESect-5.4 P-70ESect-5.4 P-71ESect-5.4 P-72ESect-5.4 P-73ESect-5.5 P-1ESect-5.5 P-2ESect-5.5 P-3ESect-5.5 P-4ESect-5.5 P-5ESect-5.5 P-6ESect-5.5 P-7ESect-5.5 P-8ESect-5.5 P-9ESect-5.5 P-10ESect-5.5 P-11ESect-5.5 P-12ESect-5.5 P-13ESect-5.5 P-14ESect-5.5 P-15ESect-5.5 P-16ESect-5.5 P-17ESect-5.5 P-18ESect-5.5 P-19ESect-5.5 P-20ESect-5.5 P-21ESect-5.5 P-22ESect-5.5 P-23ESect-5.5 P-24ESect-5.5 P-25ESect-5.5 P-26ESect-5.5 P-27ESect-5.5 P-28ESect-5.5 P-29ESect-5.5 P-30ESect-5.5 P-31ESect-5.5 P-32ESect-5.5 P-33ESect-5.5 P-34ESect-5.5 P-35ESect-5.5 P-36ESect-5.5 P-37ESect-5.5 P-38ESect-5.5 P-39ESect-5.5 P-40ESect-5.5 P-41ESect-5.5 P-42ESect-5.5 P-43ESect-5.5 P-44ESect-5.5 P-45ESect-5.5 P-46ESect-5.5 P-47ESect-5.5 P-48ESect-5.5 P-49ESect-5.5 P-50ESect-5.5 P-51ESect-5.5 P-52ESect-5.5 P-53ESect-5.5 P-54ESect-5.5 P-55ESect-5.5 P-56ESect-5.5 P-57ESect-5.5 P-58ESect-5.5 P-59ESect-5.5 P-60ESect-5.5 P-61ESect-5.5 P-62ESect-5.5 P-63ESect-5.5 P-64ESect-5.5 P-65ESect-5.5 P-66ESect-5.5 P-67ESect-5.5 P-68ESect-5.5 P-69ESect-5.5 P-70ESect-5.5 P-71ESect-5.5 P-72ESect-5.5 P-73ESect-5.5 P-74ESect-5.5 P-75ESect-5.5 P-76ESect-5.5 P-77ESect-5.5 P-78ESect-5.5 P-79ESect-5.5 P-80ESect-5.5 P-81ESect-5.5 P-82ESect-5.5 P-83ESect-5.5 P-84ESect-5.5 P-85ESect-5.5 P-86ESect-5.5 P-87ESect-5.5 P-88ESect-5.5 P-89ESect-5.5 P-90ESect-5.5 P-91ESect-5.5 P-92ESect-5.5 P-93ESect-5.5 P-94ECh-5 P-1RCCCh-5 P-2RCCCh-5 P-3RCCCh-5 P-4RCCCh-5 P-5RCCCh-5 P-6RCCCh-5 P-7RCCCh-5 P-8RCCCh-5 P-9RCCCh-5 P-1RQCh-5 P-2RQCh-5 P-3RQCh-5 P-4RQCh-5 P-5RQCh-5 P-6RQCh-5 P-7RQCh-5 P-8RQCh-5 P-9RQCh-5 P-10RQCh-5 P-11RQCh-5 P-12RQCh-5 P-13RQCh-5 P-14RQCh-5 P-15RQCh-5 P-16RQCh-5 P-17RQCh-5 P-18RQCh-5 P-1RECh-5 P-2RECh-5 P-3RECh-5 P-4RECh-5 P-5RECh-5 P-6RECh-5 P-7RECh-5 P-8RECh-5 P-9RECh-5 P-10RECh-5 P-11RECh-5 P-12RECh-5 P-13RECh-5 P-14RECh-5 P-15RECh-5 P-16RECh-5 P-17RECh-5 P-18RECh-5 P-19RECh-5 P-20RECh-5 P-21RECh-5 P-22RECh-5 P-23RECh-5 P-24RECh-5 P-25RECh-5 P-26RECh-5 P-27RECh-5 P-28RECh-5 P-29RECh-5 P-30RECh-5 P-31RECh-5 P-32RECh-5 P-33RECh-5 P-34RECh-5 P-35RECh-5 P-36RECh-5 P-37RECh-5 P-38RECh-5 P-39RECh-5 P-40RECh-5 P-41RECh-5 P-42RECh-5 P-43RECh-5 P-44RECh-5 P-45RECh-5 P-46RECh-5 P-47RECh-5 P-48RECh-5 P-49RECh-5 P-50RECh-5 P-51RECh-5 P-52RECh-5 P-53RECh-5 P-54RECh-5 P-55RECh-5 P-56RECh-5 P-57RECh-5 P-58RECh-5 P-59RECh-5 P-60RECh-5 P-61RECh-5 P-62RECh-5 P-63RECh-5 P-66RECh-5 P-69RECh-5 P-70RECh-5 P-71RECh-5 P-72RECh-5 P-1PCh-5 P-2PCh-5 P-3PCh-5 P-5PCh-5 P-6PCh-5 P-7PCh-5 P-8PCh-5 P-9PCh-5 P-10PCh-5 P-11PCh-5 P-14PCh-5 P-15PCh-5 P-18PCh-5 P-19P

Calculus: An Applied Approach (MindTap Course List)

Calculus: Early Transcendental Functions

Applied Calculus

Finite Mathematics and Applied Calculus (MindTap Course List)

Multivariable Calculus

Precalculus: Mathematics for Calculus (Standalone Book)

Calculus: Early Transcendentals

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Essentials Of Statistics

Calculus (MindTap Course List)

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Understanding Basic Statistics

Statistics for The Behavioral Sciences (MindTap Course List)

Single Variable Calculus

Probability and Statistics for Engineering and the Sciences

Intermediate Algebra

Mathematical Applications for the Management, Life, and Social Sciences

Mathematical Excursions (MindTap Course List)

Finite Mathematics

Single Variable Calculus: Early Transcendentals

Trigonometry (MindTap Course List)

Contemporary Mathematics for Business & Consumers

Elementary Technical Mathematics

Elements Of Modern Algebra

Elementary Geometry For College Students, 7e

Calculus: Early Transcendental Functions (MindTap Course List)

Calculus of a Single Variable

Elementary Geometry for College Students

Finite Mathematics for the Managerial, Life, and Social Sciences

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Multivariable Calculus

Calculus (MindTap Course List)

Study Guide for Stewart's Multivariable Calculus, 8th

Mathematics For Machine Technology

College Algebra (MindTap Course List)

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Statistics for Business & Economics, Revised (MindTap Course List)

Research Methods for the Behavioral Sciences (MindTap Course List)

Mathematics: A Practical Odyssey

Research Methods for the Behavioral Sciences (MindTap Course List)

Introduction To Statistics And Data Analysis