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

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Chapter 7.8, Problem 48E
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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 Double Integral In Exercises 45–48, use a double integral to calculate the area denoted by

∫ R ∫ d A where R is the region bounded by the given equations. See Example 6.

2 x − y + 4 = 0 ,   2 x 2 − y = 0

To determine

To calculate: The area denoted by the expression ∫R∫dA where R is the region bounded by the equations 2x−y+4=0 and 2x2−y=0 using double integral.

Explanation

Given Information:

The provided expression and the equations are ∫R∫dA, 2x−y+4=0 and 2x2−y=0 respectively.

Formula used:

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

1. 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

2. 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:

Consider the expression ∫R∫dA.

First sketch the graph of region R which is bounded by the equations 2x−y+4=0 and 2x2−y=0.

The graph of the equation 2x2−y=0 would be a parabola.

For equation 2x−y+4=0, 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,

y=2x+4=0+4=4

For x=1,

y=2x+4=2+4=6

For x=2,

y=2x+4=4+4=8

For x=3,

y=2x+4=6+4=10

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

x y=2x+4
0 4
1 6
2 8
3 10

Thus the graph of the equation 2x−y+4=0 would be a straight line

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Chapter 7.8,
Problem 47E
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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 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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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Sketch the graph of the function f(x) = {2x3ifx2x+3ifx2 and evaluate limxa+ f(x), limxaf(x), and limxaf(x) at t...

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

a Show that any function of the form y=Asinhmx+Bcoshmx Satisfies the differential equation y=m2y. b Find y=y(x)...

Calculus (MindTap Course List)

In west Texas, water is extremely important. The following data represent pH levels in groundwater for a random...

Understanding Basic Statistics

16. Explain why honesty is a hypothetical construct instead of a concrete variable. Describe how shyness might ...

Statistics for The Behavioral Sciences (MindTap Course List)

If limxa [f(x) + g(x)] = 2 and limxa [f(x) g(x)] = 1, find limxa [f(x)g(x)].

Single Variable Calculus

A special interest group has conducted a survey concerning a ban on handguns. Note: A rifle is a gun, but ills ...

Mathematical Excursions (MindTap Course List)

In Exercise 5, suppose that any incoming individual is equally likely to be assigned to any of the three statio...

Probability and Statistics for Engineering and the Sciences

For problems 27-54, simplify each of the numerical expressions. Objective 2 and 3 2(3)22(2)36(1)5

Intermediate Algebra

Calculate each expression in Exercises 124, giving the answer as a whole number or a fraction in lowest terms. ...

Finite Mathematics

72. Cell phones Cell Pro makes cell phones and has weekly costs of for rent, utilities, and equipment plus labo...

Mathematical Applications for the Management, Life, and Social Sciences

If sinx=13 and secy=54, where x and y lie between 0 and /2, evaluate sin(x + y).

Single Variable Calculus: Early Transcendentals

A four-cylinder engine has a total displacement of 1300 cm3. Find the displacement of each piston.

Elementary Technical Mathematics

Consider ABCD as shown. a How are A and C related? b How are A and B related?

Elementary Geometry For College Students, 7e

Problems 25 through 30 refer to Figure 21. Figure 21 Find B.

Trigonometry (MindTap Course List)

28. Jerry King is a server in a restaurant that pays a salary of $22 per day. He also averages tips of 18% of h...

Contemporary Mathematics for Business & Consumers

If m is an integer, show that m2 is congruent modulo 8 to one of the integers 0, 1, or 4. (Hint: Use the Divisi...

Elements Of Modern Algebra

HOW DO YOU SEE IT? Which graph, traced out only once, has a larger arc length? Explain your reasoning.

Calculus: Early Transcendental Functions (MindTap Course List)

Higher-Order Derivatives Polynomials of what degree satisfy f(n)=0? Explain your reasoning.

Calculus of a Single Variable

Provide reasons for this proof. If a=b and c=d, then a+c=b+d. Proof Statements Reasons 1. a=b 1. ? 2. a+c=b+c 2...

Elementary Geometry for College Students

SALES FORECASTING Hartman Lumber Company has two branches in the city. The sales of four of its products for th...

Finite Mathematics for the Managerial, Life, and Social Sciences

True or False? In Exercises 99-102, determine whether the statement is true or false. If it is false, explain w...

Calculus (MindTap Course List)

Finding the Equation of a Tangent Line to a CurveIn Exercises 2732, find a set of parametric equations for the ...

Calculus

Use a Table of Integrals to evaluate .

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

The graph of θ = 2 in polar coordinates is a: circle line spiral 3-leaved rose

Study Guide for Stewart's Multivariable Calculus, 8th

Cylindrical-to-Rectangular ConversionIn Exercises 38, convert the point from cylindrical coordinates to rectang...

Multivariable Calculus

Define independent, dependent, and extraneous variables and identify examples of each in an experiment.

Research Methods for the Behavioral Sciences (MindTap Course List)

Critical Thinking Determine if the statement is true or false. If the statement is false, then correct it and m...

College Algebra (MindTap Course List)

Find each base. Round the answers to 2 decimal places when necessary. 55. 712is 180% of what number?

Mathematics For Machine Technology

Describe how the reliability of a personality test could be established using the results from a correlational ...

Research Methods for the Behavioral Sciences (MindTap Course List)

Refer to exercise 15. Use Fishers LSD procedure to develop a 95% confidence interval estimate of the difference...

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

A group of ten seniors, eight juniors, six sophomores, and five freshmen must select committees are possible if...

Mathematics: A Practical Odyssey

Suppose that a random sample of 50 bottles of a particular brand of cough medicine is selected and the alcohol ...

Introduction To Statistics And Data Analysis

Home values tend to increase over time under normal conditions, but the recession of 2008 and 2009 has reported...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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