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

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Chapter 7.9, Problem 18E
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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 the Volume of a Solid Region In Exercises 13-20, use a double integral to find the volume of the solid region.

Chapter 7.9, Problem 18E, Finding the Volume of a Solid Region In Exercises 13-20, use a double integral to find the volume of

To determine

To calculate: The volume of solid region

Calculus: An Applied Approach (MindTap Course List), Chapter 7.9, Problem 18E

Explanation

Given information:

The provided solid region is

Formula used:

The procedure to calculate volume of surface z=f(x,y),

Step-1: Write the equation of surface in the form z=f(x,y)

Step-2: Sketch the projected region R in the x-y-plane.

Step-3: Determine the order of limits of integration.

Step-4: Evaluate the volume of solid region,

Volume=∫mn∫abf(x,y)dxdy

Here, the projected region is R:

m≤y≤n and a≤x≤b

Calculation:

Consider graph of solid region,

The equation of upper surface written as follow.

z=1−xy,

The following table shown different coordinate of (x,y) for y=x.

x-Coordinate y-Coordinate (x,y) Coordinate
0 0 (0,0)
1 1 (1,1)

The projected region R 0≤x≤y,0≤y≤1 in the x-y plane written as follow,

The bounds for x are 0≤x≤y and bounds for y are 0≤y≤1

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Mathematical Applications for the Management, Life, and Social Sciences

For Problems 1-50, solve each equation. Objective 1 4x3+2x=8x3x

Intermediate Algebra

For the matrices in Exercise 12, evaluate (A+B)2 and A2+2AB+B2 and compare the results.

Elements Of Modern Algebra

A selection committee consists of Ryan, Susan. and Trevor. To decide on issues, they use a one-person, one-vote...

Mathematical Excursions (MindTap Course List)

Find sec if tan=815 and terminates in QIII.

Trigonometry (MindTap Course List)

A plane flies 60.45 mi due north, then flies 102.3 mi due east. Find the area of a rectangle formed by these di...

Elementary Technical Mathematics

According to the Food and Nutrition Service of the U.S. Department of Agriculture, in one school year the Natio...

Contemporary Mathematics for Business & Consumers

In the figure, assume that a 0. Prove that BDDEBEAC.

Elementary Geometry For College Students, 7e

Finding a Limit In Exercises 5-22. find the limit. limx9(4x1)

Calculus of a Single Variable

Each integral represents the volume of a solid. Describe the solid. 0sinxdx

Single Variable Calculus: Early Transcendentals

Finding and Evaluating Partial Derivatives In Exercises 45-52, find fx and fy and evaluate each at the given po...

Calculus: Early Transcendental Functions (MindTap Course List)

In Exercises 19 to 26, solve each equation by using the Quadratic Formula. Give exact solutions in simplified f...

Elementary Geometry for College Students

Find the accumulated amount A if 327.35 is invested at the interest rate of 513/year compounded daily for 7 yea...

Finite Mathematics for the Managerial, Life, and Social Sciences

Precalculus or Calculus In Exercises 3-6.decide whether the problem can be solved using precalculus or whether ...

Calculus

Maximum Volume Use Lagrange multipliers to find the dimensions of a rectangular box of maximum volume that can ...

Multivariable Calculus

What is the number of the integral formula in your texts Table of Integrals that may be used to evaluate dxx2x2...

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

If (a, b) is a critical point of f(x, y), all second derivatives of f are continuous, and fxx(a, b) = 10, fyy(a...

Study Guide for Stewart's Multivariable Calculus, 8th

Perform all operations. Give all answers in a+bi form. 5-6i-7+4i

College Algebra (MindTap Course List)

Describe how differential attrition and communication between participants can threaten the internal validity o...

Research Methods for the Behavioral Sciences (MindTap Course List)

Suppose that Blue Cab operates 15% of the taxis in a certain city and Green Cab operates the other 85%. After a...

Introduction To Statistics And Data Analysis

Describe the two general problems (observer influence and subjectivity) that can exist with behavioral observat...

Research Methods for the Behavioral Sciences (MindTap Course List)

A sample of 16 items from population 1 has a sample variance s12=5.8 and a sample of 21 items from population 2...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

The FinancialTimes/Harris Poll is a monthly online poll of adults from six countries in Europe and the United S...

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

Read the setting of these metric micrometer scales graduated in 0.01 mm.

Mathematics For Machine Technology

HOW DO YOU SEE IT? Use the graph of the surface to determine the sign of each partial derivative. Explain your ...

Calculus (MindTap Course List)

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