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

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Chapter 7.8, Problem 34E
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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 31-36, use a double integral to find the area of the region bounded by the graphs of the equations. See Example 4.

x + y = 2 ,     x = 0 ,   y = 0

To determine

To calculate: The area of the region bounded by graph of equation x+y=2 and x=0,y=0 by using double integration.

Explanation

Given Information:

The provided equations are x+y=2 and x=0,y=0.

Formula used:

If a region is R defined in the domain of a≤y≤b and c≤x≤d, then,

The area of the region R is,

A=∫cd∫abdydx

Calculation:

Consider the equations,

x+y=2 and x=0,y=0.

The graph of region bounded by x+y=2 and x=0,y=0 is shown below.

Solve the equation x+y=2 for y.

y=2−xy=(2−x)2

The bounds for x are 0≤x≤4 and bounds for y are 0≤y≤(2−x)2.

The area of the region is

A=∫04∫0(2−x)2dydx

Integrate with respect to y by holding x constant,

∫04∫0(2−x)2dydx=∫04[y]0(2−

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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
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A survey was completed by individuals who were currently on the Zone diet (Z). the South Beach diet (S), or the...

Mathematical Excursions (MindTap Course List)

When X1, X2,, Xn are independent Poisson variables, each with parameter . and n is large, the sample mean X has...

Probability and Statistics for Engineering and the Sciences

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Elementary Technical Mathematics

In problems 7-10, replace each radical with a fractional exponent.Do not simplify. 9.

Mathematical Applications for the Management, Life, and Social Sciences

Find the value of the sum. 23. j=163j+1

Single Variable Calculus: Early Transcendentals

Given: ABDCABDC C is the midpoint of BE Prove: ACDE

Elementary Geometry For College Students, 7e

13. Let be an abelian group with respect to multiplication. Prove that each of the following subsets of is ...

Elements Of Modern Algebra

As one of the loan officers for Grove Gate Bank, calculate the monthly principal and interest PI, using Table 1...

Contemporary Mathematics for Business & Consumers

Physiology In the human body, the value of that makes the following expression zero is the angle at which an a...

Trigonometry (MindTap Course List)

Convergence or Divergence In Exercises 5360, use the results of Exercises 4952 to determine whether the imprope...

Calculus of a Single Variable

Using the Alternative Form of the Derivative In Exercises 69-76, use the alternative form of the derivative to ...

Calculus: Early Transcendental Functions (MindTap Course List)

Draw and describe the locus of points in the plane that are equidistant from the sides of ABC. ________________...

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In Exercises 8994, determine whether the statement is true or false. If it is true, explain why it is true. If ...

Finite Mathematics for the Managerial, Life, and Social Sciences

Minimum Surface Area Use Lagrange multipliers to find the dimensions of a right circular cylinder with volume V...

Calculus

Power Series Solution In Exercises 59 and 60, use a power series to solve the differential equation. y+3xy3y=0

Multivariable Calculus

CONCEPT CHECK Domains of Hyperbolic Functions Which hyperbolic functions have domains that are not all real num...

Calculus (MindTap Course List)

2 1 0 does not exist

Study Guide for Stewart's Multivariable Calculus, 8th

If f(x) = sin 2x, an upper bound for |f(n + 1)(x)| is 2 2n 2n + 1 22n

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

Practice Find the slope of the line passing through each pair of points, if possible. P(4,3);Q(4,3)

College Algebra (MindTap Course List)

consider the following hypothesis test: H0: 20 Ha: 20 A sample of 50 provided a sample mean of 19.4. The po...

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

A manufacturer is considering purchasing parts from three different suppliers. The parts received from the supp...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Identify the three primary techniques for limiting confounding by individual differences in between-subjects ex...

Research Methods for the Behavioral Sciences (MindTap Course List)

Determine the nearer fractional equivalents of each of the following decimals using the decimal equivalent tabl...

Mathematics For Machine Technology

The Bloomberg web site included the data in the accompanying table on the number of movies made by 25 Saturday ...

Introduction To Statistics And Data Analysis

Define and compute the three measures of central tendency.

Research Methods for the Behavioral Sciences (MindTap Course List)

Of all workers at a certain factory, the proportions earning certain hourly wages are as shown in figure 3.30. ...

Mathematics: A Practical Odyssey

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