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

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Chapter 7.8, Problem 36E
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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.

y = 4 − x 2 ,     y = x + 2

To determine

To calculate: The area of the region bounded by graph of equations y=4−x2 and y=x+2 by using double integration.

Explanation

Given Information:

The provided equations are y=4−x2 and y=x+2.

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,

y=x,y=2x and x=2.

The graph of region bounded by the equation y=4−x2 and y=x+2 is shown in below.

The point of intersection of the two graph is found by equating y=4−x2 and y=x+2,

4−x2=x+2x2+x−2=0

Factor the above quadratic equation,

x2+2x−x−2=0x(x+2)−1(x+2)=0(x+2)(x−1)=0

Therefore,

x=1 and x=−2

The point of intersection of the two graphs y=4−x2 and y=x+2 is (−2,0) and (1,3).

The bounds for x are −2≤x≤1 and bounds for y are 4−x2≤y≤x+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
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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Brunt, Rhee, and Zhong (2008) surveyed 557 undergraduate college students to examine their weight status, healt...

Statistics for The Behavioral Sciences (MindTap Course List)

Change each decimal to a percent: 1.2

Elementary Technical Mathematics

For Problems 27-36, simplify each of the algebraic expressions by combining similar terms. 3(2n2+1)+4(n25)

Intermediate Algebra

In problem 18 and 19, determine whether each graph represents as a function of . 19.

Mathematical Applications for the Management, Life, and Social Sciences

Find a Route The following map shows the 10 bridges and 3 islands between the suburbs of North Bay and South Ba...

Mathematical Excursions (MindTap Course List)

The May 1, 2009, issue of The Montclarian reported the following home sale amounts for a sample of homes in Ala...

Probability and Statistics for Engineering and the Sciences

Determine whether the sequence converges or diverges. If it converges, find the limit. 36. an(1)n+1nn+n

Single Variable Calculus: Early Transcendentals

Prove: If ab=cd where b0 and d0, then a+bb=c+dd.

Elementary Geometry For College Students, 7e

Add the following numbers. 2,3598,511+14,006_

Contemporary Mathematics for Business & Consumers

10. Find all normal subgroups of the octic group.

Elements Of Modern Algebra

Graph one complete cycle of each of the following. In each case, label the axes accurately and identify the per...

Trigonometry (MindTap Course List)

Find two vectors in opposite directions that are orthogonal to the vector u. u=9i4j

Calculus: Early Transcendental Functions (MindTap Course List)

Evaluating a Definite Integral Using a Geometric Formula In Exercises 23-32, sketch the region whose area is gi...

Calculus of a Single Variable

HOME HEALTH-CARE AND EQUIPMENT SPENDING The following table gives the projected spending on home care and durab...

Finite Mathematics for the Managerial, Life, and Social Sciences

In Exercises 37 to 43, angle measures should be given to the nearest degree; distance should be given to the ne...

Elementary Geometry for College Students

Finding a Particular Solution: Initial Conditions In Exercises 29-32, use a characteristic equation to find the...

Multivariable Calculus

Evaluating a Definite Integral In Exercises 69-74, evaluate the definite integral using any method. Use a graph...

Calculus

True or False: The curve at the right appears to be piecewise smooth.

Study Guide for Stewart's Multivariable Calculus, 8th

True or False: y = xex is a solution to y=y+yx.

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

Finding a Derivative In Exercises 7-26. use the rules of differentiation to find the derivative of the function...

Calculus (MindTap Course List)

Briefly explain what is meant when a researcher reports a significant mean difference between two treatment con...

Research Methods for the Behavioral Sciences (MindTap Course List)

Data showing the population by state in millions of people follow (The World Almanac, 2012). a. Develop a frequ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Consider the following data for a dependent variable y and two independent variables, x1 and x2. x1 x2 y 30 12 ...

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

In an open market, the selling price of a product is determined by the supply of the product and the demand of ...

Mathematics: A Practical Odyssey

Solve each of the following equations using either the multiplication, root, or power principal of equality. Ch...

Mathematics For Machine Technology

Define the validity of measurement and explain why and how it is measured.

Research Methods for the Behavioral Sciences (MindTap Course List)

Use the information given in the previous exercise to construct and interpret a 95% confidence interval for the...

Introduction To Statistics And Data Analysis

Write each expression without using absolute value symbols. 32

College Algebra (MindTap Course List)

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