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

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Chapter 7, Problem 89RE
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Calculus: An Applied Approach (Min...

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Ron Larson
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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 = 10 − x 2 ,   y = 6

To determine

To calculate: The area of the region bounded by the graph of the equations y=10−x2 and y=6 using double integral.

Explanation

Given Information:

The provided the graph of the equations are y=10−x2 and y=6.

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=10−x2 and y=6.

The graph of the equation y=6 would be a horizontal line.

For equation y=10−x2, 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 is;

y=10−x2=10−0=10

For x=1 the value of y is;

y=10−x2=10−1=9

For x=2 the value of y is;

y=10−x2=10−22=6

For x=3

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Finite Mathematics and Applied Calculus (MindTap Course List)

For the following set of scores, find the value of each expression: a. X b. (X)2 c. X2 d. (X +3)

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

You are the automotive specialist for the monthly magazine Consumer Beware. Part of your job is to investigate ...

Essentials Of Statistics

A movie theater has been charging 10.00 per person and selling about 500 tickets on a typical weeknight. After ...

Calculus (MindTap Course List)

In Exercises 47-50, determine whether the statement is true or false. If it is true, explain why it is true. If...

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

Expand Your Knowledge: Dotplot another display technique that is somewhat similar to histogram is dotplot. In a...

Understanding Basic Statistics

A sample of n=16 scores has a mean of M=56and a standard deviation of s=12 . a. Explain what is measured by the...

Statistics for The Behavioral Sciences (MindTap Course List)

Explain why the function is discontinuous at the given number a. Sketch the graph of the function. 17. f(x)=1x+...

Single Variable Calculus

For Problems 51-66, use an algebraic approach to solve each problem. Objective 2 If 15 is subtracted from three...

Intermediate Algebra

Describe the set of points (x,y) such that x2+y2=9.

Finite Mathematics

In Exercises 25 and 26, determine whether the first set is a subset of the second set. 25. {0, 1, 5, 9}, the se...

Mathematical Excursions (MindTap Course List)

Let X1, X2,, Xn be a random sample from a uniform distribution on the interval [0, ), so that f(x)={10x0otherwi...

Probability and Statistics for Engineering and the Sciences

In problems 31-42, let. And be the universal set of natural numbers less than 11.Find the following. 40. ...

Mathematical Applications for the Management, Life, and Social Sciences

Water in an open bowl evaporates at a rate proportional to the area of the surface of the water. (This means th...

Single Variable Calculus: Early Transcendentals

Prove each identity. sin(32+x)+sin(32x)=2cosx

Trigonometry (MindTap Course List)

21. The Bean Counters, an accounting firm, has 161 employees. If of them are certified public accountants, how...

Contemporary Mathematics for Business & Consumers

Which is larger? 1 gram or 1 milligram

Elementary Technical Mathematics

Find a such that the points A1,3, B4,5, and Ca,a are collinear.

Elementary Geometry For College Students, 7e

3. Let be a set of three elements given by . In the following table, all of the elements of are listed in a r...

Elements Of Modern Algebra

WRITING ABOUT CONCEPTS Witting Equations In Exercises 73 and 74, write an equation whose graph has the indicate...

Calculus: Early Transcendental Functions (MindTap Course List)

Using the Integral Test In Exercises 3-22, confirm that the Integral Test can be applied to the series. Then us...

Calculus of a Single Variable

Repeat Exercise 31 for the augmented matrix of Exercise 28 31. Write a system of linear equations for the augme...

Finite Mathematics for the Managerial, Life, and Social Sciences

What type of angle has the given measure? a 115 b 180 c 30

Elementary Geometry for College Students

Finding a Limit In Exercises 17-36, find the limit, if it exists. limxxcosxx

Calculus

Finding a Limit In Exercises 21-24, find the limit. limxtanhx

Calculus (MindTap Course List)

Comparing PlanesIn Exercises 6974, determine whether the planes are parallel, orthogonal, or neither. If they a...

Multivariable Calculus

True or False: If converges and converges, then converges.

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

Use the Taylor polynomial of degree 2 for centered at 1 to estimate . 1.250 1.255 1.265 1.270

Study Guide for Stewart's Multivariable Calculus, 8th

For each of the following problems, substitute the given values in the formula and solve for the unknown. Check...

Mathematics For Machine Technology

A market research firm conducts telephone surveys with a 40% historical response rate. What is the probability ...

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

For the Hawkins Company, the monthly percentages of all shipments received on time over the past 12 months are ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Each of the following studies examines the relationship between sugar consumption and activity level for presch...

Research Methods for the Behavioral Sciences (MindTap Course List)

Describe how the concept of participant reactivity might explain why a persons behavior in a group of strangers...

Research Methods for the Behavioral Sciences (MindTap Course List)

A survey of a representative sample of 478 U.S. employers determined that 359 ranked stress as then-top health ...

Introduction To Statistics And Data Analysis

Self Check Factor: 8a3+1000b6.

College Algebra (MindTap Course List)

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