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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 7, Problem 92RE
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Finding Area with a Double Integral In Exercises 89–92, use a double integral to find the area of the region bounded by the graphs of the equations.

y = x 2 − 2 x − 2 ,   y = − x

To determine

To calculate: The area of the region bounded by the graph of the equations y=x2−2x−2 and y=−x using double integral.

Explanation

Given Information:

The provided the graph of the equations are y=x2−2x−2 and y=−x.

Formula used:

To determine the area in the plane by double integrals mostly two kind of strips are used.

Vertical strip: In case of vertical strip shown below the region bounded is given by;

a≤x≤bg1(x)≤y≤g2(x)

And the area of the region is given by;

∫ab∫g1(x)g2(x)dydx

Horizontal strip: In case of horizontal strip shown below the region bounded is given by,

c≤y≤dh1(y)≤y≤h2(y)

And the area of the region is given by;

∫cd∫h1(y)h2(y)dxdy

Calculation:

First sketch the graph of region R which is bounded by the equations y=x2−2x−2 and y=−x.

The graph of the equation y=−x would be a straight line.

For equation y=x2−2x−2, put different values of x in the equation to obtain different values of y in order to plot graph of the equation.

For x=0 the value of y=x2−2x−2 is;

y=x2−2x−2=0−0−2=−2

For x=1 the value of y=x2−2x−2 is;

y=x2−2x−2=1−2−2=−3

For x=2 the value of y=x2−2x−2 is;

y=x2−2x−2=4−4−2=−2

For x=3 the value of y=x2−2x−2 is;

y=x2−2x−2=9−6−2=1

Now construct a table showing different values of x and y as;

x y=x+3
0 −2
1 −3
2 −2
3 1

The graph of the equation y=x2−2x−2 and y=−x is shown below as;

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Sect-7.1 P-1CPSect-7.1 P-2CPSect-7.1 P-3CPSect-7.1 P-4CPSect-7.1 P-5CPSect-7.1 P-6CPSect-7.1 P-7CPSect-7.1 P-1SWUSect-7.1 P-2SWUSect-7.1 P-3SWU
Sect-7.1 P-4SWUSect-7.1 P-5SWUSect-7.1 P-6SWUSect-7.1 P-7SWUSect-7.1 P-8SWUSect-7.1 P-1ESect-7.1 P-2ESect-7.1 P-3ESect-7.1 P-4ESect-7.1 P-5ESect-7.1 P-6ESect-7.1 P-7ESect-7.1 P-8ESect-7.1 P-9ESect-7.1 P-10ESect-7.1 P-11ESect-7.1 P-12ESect-7.1 P-13ESect-7.1 P-14ESect-7.1 P-15ESect-7.1 P-16ESect-7.1 P-17ESect-7.1 P-18ESect-7.1 P-19ESect-7.1 P-20ESect-7.1 P-21ESect-7.1 P-22ESect-7.1 P-23ESect-7.1 P-24ESect-7.1 P-25ESect-7.1 P-26ESect-7.1 P-27ESect-7.1 P-28ESect-7.1 P-29ESect-7.1 P-30ESect-7.1 P-31ESect-7.1 P-32ESect-7.1 P-33ESect-7.1 P-34ESect-7.1 P-35ESect-7.1 P-36ESect-7.1 P-37ESect-7.1 P-38ESect-7.1 P-39ESect-7.1 P-40ESect-7.1 P-41ESect-7.1 P-42ESect-7.1 P-43ESect-7.1 P-44ESect-7.2 P-1CPSect-7.2 P-2CPSect-7.2 P-3CPSect-7.2 P-1SWUSect-7.2 P-2SWUSect-7.2 P-3SWUSect-7.2 P-4SWUSect-7.2 P-5SWUSect-7.2 P-6SWUSect-7.2 P-1ESect-7.2 P-2ESect-7.2 P-3ESect-7.2 P-4ESect-7.2 P-5ESect-7.2 P-6ESect-7.2 P-7ESect-7.2 P-8ESect-7.2 P-9ESect-7.2 P-10ESect-7.2 P-11ESect-7.2 P-12ESect-7.2 P-13ESect-7.2 P-14ESect-7.2 P-15ESect-7.2 P-16ESect-7.2 P-17ESect-7.2 P-18ESect-7.2 P-19ESect-7.2 P-20ESect-7.2 P-21ESect-7.2 P-22ESect-7.2 P-23ESect-7.2 P-24ESect-7.2 P-25ESect-7.2 P-26ESect-7.2 P-27ESect-7.2 P-28ESect-7.2 P-35ESect-7.2 P-36ESect-7.2 P-37ESect-7.2 P-38ESect-7.2 P-39ESect-7.2 P-40ESect-7.2 P-41ESect-7.2 P-42ESect-7.2 P-43ESect-7.2 P-44ESect-7.2 P-45ESect-7.2 P-46ESect-7.2 P-47ESect-7.2 P-48ESect-7.2 P-49ESect-7.2 P-50ESect-7.2 P-51ESect-7.3 P-1CPSect-7.3 P-2CPSect-7.3 P-3CPSect-7.3 P-4CPSect-7.3 P-5CPSect-7.3 P-1SWUSect-7.3 P-2SWUSect-7.3 P-3SWUSect-7.3 P-4SWUSect-7.3 P-5SWUSect-7.3 P-6SWUSect-7.3 P-7SWUSect-7.3 P-8SWUSect-7.3 P-9SWUSect-7.3 P-10SWUSect-7.3 P-1ESect-7.3 P-2ESect-7.3 P-3ESect-7.3 P-4ESect-7.3 P-5ESect-7.3 P-6ESect-7.3 P-7ESect-7.3 P-8ESect-7.3 P-9ESect-7.3 P-10ESect-7.3 P-11ESect-7.3 P-12ESect-7.3 P-13ESect-7.3 P-14ESect-7.3 P-15ESect-7.3 P-16ESect-7.3 P-17ESect-7.3 P-18ESect-7.3 P-19ESect-7.3 P-20ESect-7.3 P-21ESect-7.3 P-22ESect-7.3 P-23ESect-7.3 P-24ESect-7.3 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P-20QYSect-7.5 P-21QYSect-7.5 P-22QYSect-7.5 P-23QYSect-7.5 P-24QYSect-7.5 P-25QYSect-7.5 P-26QYSect-7.6 P-1CPSect-7.6 P-2CPSect-7.6 P-3CPSect-7.6 P-4CPSect-7.6 P-1SWUSect-7.6 P-2SWUSect-7.6 P-3SWUSect-7.6 P-4SWUSect-7.6 P-5SWUSect-7.6 P-6SWUSect-7.6 P-7SWUSect-7.6 P-8SWUSect-7.6 P-9SWUSect-7.6 P-10SWUSect-7.6 P-1ESect-7.6 P-2ESect-7.6 P-3ESect-7.6 P-4ESect-7.6 P-5ESect-7.6 P-6ESect-7.6 P-7ESect-7.6 P-8ESect-7.6 P-9ESect-7.6 P-10ESect-7.6 P-11ESect-7.6 P-12ESect-7.6 P-13ESect-7.6 P-14ESect-7.6 P-15ESect-7.6 P-16ESect-7.6 P-17ESect-7.6 P-18ESect-7.6 P-19ESect-7.6 P-20ESect-7.6 P-21ESect-7.6 P-22ESect-7.6 P-23ESect-7.6 P-24ESect-7.6 P-25ESect-7.6 P-26ESect-7.6 P-27ESect-7.6 P-28ESect-7.6 P-29ESect-7.6 P-30ESect-7.6 P-31ESect-7.6 P-32ESect-7.6 P-33ESect-7.6 P-34ESect-7.6 P-35ESect-7.6 P-36ESect-7.6 P-37ESect-7.6 P-38ESect-7.6 P-39ESect-7.6 P-40ESect-7.6 P-41ESect-7.6 P-42ESect-7.6 P-43ESect-7.6 P-44ESect-7.6 P-45ESect-7.7 P-1CPSect-7.7 P-2CPSect-7.7 P-3CPSect-7.7 P-1SWUSect-7.7 P-2SWUSect-7.7 P-3SWUSect-7.7 P-4SWUSect-7.7 P-5SWUSect-7.7 P-6SWUSect-7.7 P-7SWUSect-7.7 P-8SWUSect-7.7 P-1ESect-7.7 P-2ESect-7.7 P-3ESect-7.7 P-4ESect-7.7 P-5ESect-7.7 P-6ESect-7.7 P-7ESect-7.7 P-8ESect-7.7 P-9ESect-7.7 P-10ESect-7.7 P-11ESect-7.7 P-12ESect-7.7 P-13ESect-7.7 P-14ESect-7.7 P-15ESect-7.7 P-16ESect-7.7 P-17ESect-7.7 P-18ESect-7.7 P-19ESect-7.7 P-20ESect-7.7 P-21ESect-7.7 P-22ESect-7.7 P-23ESect-7.7 P-24ESect-7.7 P-25ESect-7.7 P-26ESect-7.7 P-27ESect-7.7 P-28ESect-7.7 P-29ESect-7.7 P-30ESect-7.8 P-1CPSect-7.8 P-2CPSect-7.8 P-3CPSect-7.8 P-4CPSect-7.8 P-5CPSect-7.8 P-6CPSect-7.8 P-1SWUSect-7.8 P-2SWUSect-7.8 P-3SWUSect-7.8 P-4SWUSect-7.8 P-5SWUSect-7.8 P-6SWUSect-7.8 P-7SWUSect-7.8 P-8SWUSect-7.8 P-9SWUSect-7.8 P-10SWUSect-7.8 P-11SWUSect-7.8 P-12SWUSect-7.8 P-13SWUSect-7.8 P-14SWUSect-7.8 P-15SWUSect-7.8 P-16SWUSect-7.8 P-1ESect-7.8 P-2ESect-7.8 P-3ESect-7.8 P-4ESect-7.8 P-5ESect-7.8 P-6ESect-7.8 P-7ESect-7.8 P-8ESect-7.8 P-9ESect-7.8 P-10ESect-7.8 P-11ESect-7.8 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Calculus: Early Transcendental Functions

Use a graphing device as in Example 4 (or Newtons method or solve numerically using a calculator or computer) t...

Multivariable Calculus

Average In a class of 25 students, the average score is 84. Six students in the class each received a maximum s...

Precalculus: Mathematics for Calculus (Standalone Book)

Describe the level surfaces of the function. 68. f(x, y, z) = x2 + 3y2 + 5z2

Calculus: Early Transcendentals

A variety of information has been collected for all district high schools. Find the most appropriate measure of...

Essentials Of Statistics

Construct a frequency distribution table for the following set of scores. Include columns for proportion and pe...

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

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

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Calculus (MindTap Course List)

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Statistics for The Behavioral Sciences (MindTap Course List)

Interpretation Lucy conducted a survey asking some of her friends to specify their favorite type of TV entertai...

Understanding Basic Statistics

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Single Variable Calculus

Convert the expressions in Exercises 6584 to power form. 18xx23x35

Finite Mathematics

For Problems 5-54, perform the following operations with real numbers. Objectives 3-6 (8)(13)

Intermediate Algebra

In problems 23-58, perform the indicated operations and simplify. 39.

Mathematical Applications for the Management, Life, and Social Sciences

Based on data from a dart-throwing experiment, the article Shooting Darts (Chance, Summer 1997, 1619)proposed t...

Probability and Statistics for Engineering and the Sciences

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Mathematical Excursions (MindTap Course List)

Sketch the graph of a function that satisfies all of the given conditions. f(0) =f(4) = 0, f(x) = 1 if x 1, f(...

Single Variable Calculus: Early Transcendentals

Add the following hexadecimal numbers. Check using decimals. AAA+BCE

Elementary Technical Mathematics

Solve each equation for if 0360. 2csc+5=3

Trigonometry (MindTap Course List)

34. On May 1. Emerson Fast bought 10 Manitoba Polar bonds with a coupon rate of . The purchase price was 101.37...

Contemporary Mathematics for Business & Consumers

Let f=(1,2,3)(4,5). Compute each of the following powers of f. a. f1 b. f18 c. f23 d. f201

Elements Of Modern Algebra

In Exercises 17 to 22, draw an ideally placed figure in the coordinate system; then name the coordinates of eac...

Elementary Geometry For College Students, 7e

Verifying an Inconclusive Test In Exercise 99-102, verify that the Ratio Teat is Inconclusive for the p -series...

Calculus: Early Transcendental Functions (MindTap Course List)

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Calculus of a Single Variable

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Elementary Geometry for College Students

Gasoline Sales Gloria Newburg operates three self-service gasoline stations in different parts of town.On a cer...

Finite Mathematics for the Managerial, Life, and Social Sciences

True or False: is a convergent series.

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

Building Design Concrete sections for a new building have the dimensions (in meters) and shape shown in the fig...

Calculus

Inverse Function Let f(x)=x2x1 Show that f is its own inverse function. What can you conclude about the graph o...

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AreaIn Exercises 4146, use a double integral to find the area of the shaded region.

Multivariable Calculus

The absolute minimum of f(x, y) = 40 − 3x2 − 2y2 with domain D = {(x, y)| −2 ≤ x ≤ 3, −1 ≤ y ≤ 2} is: 0 5 12 40...

Study Guide for Stewart's Multivariable Calculus, 8th

Explain the distinction between naturalistic observation and participant observation, and describe the situatio...

Research Methods for the Behavioral Sciences (MindTap Course List)

Fill in the blanks. An equation of the form ax+b=0 is called a ______ equation.

College Algebra (MindTap Course List)

Pessimists commonly claim that, if you drop a piece of buttered bread, it will probably land butter-side down. ...

Research Methods for the Behavioral Sciences (MindTap Course List)

Major League Baseball (MLB) includes two groups of teams, in leagues. There are 15 teams in each of the America...

Introduction To Statistics And Data Analysis

Are nursing salaries in Tampa, Florida, lower than those in Dallas, Texas? As reported by the Tampa Tribune, sa...

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

Initial public offerings (IPOs) of stocks are on average underpriced. The standard deviation measures the dispe...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Three views of the angular portion of a tool with front clearance are shown. A pictorial view with auxiliary li...

Mathematics For Machine Technology

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