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

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Chapter 7.9, Problem 7E
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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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Comparing Different Orders of Integration In Exercises 7-12, set up the integrals for both orders of integration and use the more convenient order to find the volume of the solid region bounded by the surface f(x, y) and the planes. See Example 2.

f ( x , y ) = x y

Planes: z = 0 , y = 0 , y = 5 , x = 0 , x = 3

To determine

To calculate: The volume of the function f(x,y)=xy by representing its integral for both orders.

Explanation

Given Information:

Function is f(x,y)=xy and points are z=0,y=0,x=0,x=3,y=5.

Formula used:

Standard form of volume integral,

V=∫∫f(x,y)dxdy

Calculation:

Consider the volume integral,

V=∫∫xy dxdy

Consider case 1:

(1)∫x=03(∫05xydy)dx  

Consider case 2:

(2)∫y=05</

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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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Find all degree solutions. tan23=3

Trigonometry (MindTap Course List)

Proof Prove that if f is differentiable on (,) and f(x)1 for all real numbers, then f has at most one fixed poi...

Calculus of a Single Variable

Finding a Limit In Exercises 25-36, find the limit (if it exists). If the limit does not exist, explain why. li...

Calculus: Early Transcendental Functions (MindTap Course List)

Find f. f(x)=(x+1)/x, f(1) = 5

Single Variable Calculus: Early Transcendentals

In Exercises 1-8, find the amount future value of each ordinary annuity. 150/month for 15 years at 6/year compo...

Finite Mathematics for the Managerial, Life, and Social Sciences

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Elementary Geometry for College Students

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

Calculus

If 2x + 2 ≤ f(x) ≤ x2 + 3 for all x, then =_____. 1 4 does not exist exists but cannot be determined from the ...

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

The length of the are r = eθ for 0 ≤ θ ≤ π is given by:

Study Guide for Stewart's Multivariable Calculus, 8th

Domain and Continuity In Exercises 1-4, (a) find the domain of r, and (b) determine the interval(s) on which th...

Multivariable Calculus

Graph each polynomial function. f(x)=4x34x2x+1

College Algebra (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

Solve the following exercises. Compute angles to the nearer minute in triangles with customary unit sides. Comp...

Mathematics For Machine Technology

In addition to the key words that were defined in the text, you should be able to define the following terms, w...

Research Methods for the Behavioral Sciences (MindTap Course List)

For each of the following scenarios, identify which sampling method is used: a. The State College is conducting...

Research Methods for the Behavioral Sciences (MindTap Course List)

In automobile mileage and gasoline-consumption testing, 13 automobiles were road tested for 300 miles in both c...

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

The following partially completed ANOVA table approximately matches summary statistics given in the article Fro...

Introduction To Statistics And Data Analysis

CurvatureVerify that the curvature at any point (x,y) on the graph of y=coshx is 1/y2.

Calculus (MindTap Course List)

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