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

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Chapter 7.8, Problem 37E
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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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Changing the Order of Integration In Exercises 37-44, sketch the region R whose area is given by the double integral. Then change the order of integration and show that both orders yield the same value. See Example 5.

∫ 0 1 ∫ 0 2 d y   d x

To determine

To graph: The region whose area is given by double integration ∫01∫02dydx, the change the order of integration and shows both orders yield same value.

Explanation

Given Information:

The provided double integration is ∫01∫02dydx.

Graph:

Consider the double integration,

∫01∫02dydx.

From limits of integration, the bounds for x are 0≤x≤1 and bounds for y are 0≤y≤2.

The graph of region bounded by 0≤x≤1 and 0≤y≤2 is shown in below,

The area for the region 0≤x≤1 and 0≤y≤2 is

∫01∫02dydx

Evaluate the above integration integrate with respect to y by holding x constant,

∫01∫02dydx=∫01[y]02dx

Now, replace the y by limit of integration,

∫01[y]02dx=∫01[2]dx

Evaluate the above integration integrate with respect to x by holding y constant,

∫01[2]dx=[2x]01

Now, replace the x by limit of integration,

[2x]01=2

Now change the order of integration dydx to dxdy

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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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Finite Mathematics

General: Thumbtack Drop a thumbtack and observe how it lands. (a) Describe how you could use a relative frequen...

Understanding Basic Statistics

Health insurance cost The per capita net cost C (in dollars) of private health insurance coverage in the United...

Mathematical Applications for the Management, Life, and Social Sciences

Simplify the algebraic expressions in Problems 15-34 by removing parentheses and combining similar terms. Objec...

Intermediate Algebra

I have three errands to take care of in the Administration Building. Let Xi = the time that it takes for the it...

Probability and Statistics for Engineering and the Sciences

In Exercises 17 and 18, use the given information to find the number of elements in each of the regions labeled...

Mathematical Excursions (MindTap Course List)

Fill in each blank: 6000floz=gal

Elementary Technical Mathematics

Use the guidelines of Section 4.5 to sketch the curve. y = 2 2x x3

Single Variable Calculus: Early Transcendentals

Find all primitive sixth roots of . Find all primitive eighth roots of .

Elements Of Modern Algebra

For Questions 1 through 10, fill in the blank with an appropriate word or number. The number i, called the ____...

Trigonometry (MindTap Course List)

Compute the principal for the following loans. Use ordinary interest when time is stated in days. Principal Rat...

Contemporary Mathematics for Business & Consumers

Find the values of x in each proportion: a x6=3x c 6x+4=2x+2 b x53=2x37 d x+35=x+57 e x2x5=2x+1x1 g x1x+2=103x2...

Elementary Geometry For College Students, 7e

Finding the Volume of a Solid In Exercises 23-26, use the shell method to find the volume of the solid generate...

Calculus of a Single Variable

Using Absolute Value In Exercises 173-176, use the result of Exercise 172 to find the derivative of the functio...

Calculus: Early Transcendental Functions (MindTap Course List)

Fill in the blanks. a. The point P(a,0) lies on the _ axis, and the point P(0,b) lies on the _ axis. b. If the ...

Finite Mathematics for the Managerial, Life, and Social Sciences

aHow are S and V related? bFind mV if mS=73. Exercises 18,19

Elementary Geometry for College Students

Graphing a Parametric Surface In Exercises 1316, use a computer algebra system to graph the surface represented...

Multivariable Calculus

The y-coordinate of the center of mass of a lamina D with density ρ(x, y) and mass m is:

Study Guide for Stewart's Multivariable Calculus, 8th

ex(ex)2 = a) ex3 b) e3x c) 3ex d) e4x

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

Using the Quotient Rule In Exercises 11-16. use the Quotient Rule to find the derivative of the function. f(t)=...

Calculus

Finding a Derivative In Exercises 5-20, find dy / dx by implicit differentiation. 2x3+3y3=64

Calculus (MindTap Course List)

Cars arrive at a car wash randomly and independently; the probability of an arrival is thesame for any two time...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Fill in the blanks. logbMN= logb_______+logb_______

College Algebra (MindTap Course List)

The sales manager of a large company selected a random sample of n = 10 salespeople and determined for each one...

Introduction To Statistics And Data Analysis

In the following exercises, you will explore some of your calculators graphing capabilities. Answers are not gi...

Mathematics: A Practical Odyssey

Information about mutual funds provided by Morningstar includes the type of mutual fund (Domestic Equity, Inter...

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

Define experimenter bias, demand characteristics, and reactivity, and explain how these artifacts can threaten ...

Research Methods for the Behavioral Sciences (MindTap Course List)

Find dimension x. All dimensions are in inches.

Mathematics For Machine Technology

Describe the two nonexperimental nonequivalent group designs (differential research and the posttest-only noneq...

Research Methods for the Behavioral Sciences (MindTap Course List)

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