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

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Chapter 7.9, Problem 11E
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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 ) = 1 x 2 + 4

Planes: z = 0 , y = 0 , y = 3 x , x = 1

To determine

To calculate: The volume of solid region bounded by surface f(x,y)=1x2+4 and plane: z=0,y=0,y=3x,x=1.

Explanation

Given information:

The provided equation of surface f(x,y)=1x2+4 and plane is z=0,y=0,y=3x,x=1.

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 equation of surface,

f(x,y)=1x2+4

The region R: z=0,y=0,y=3x,x=1

The following table shown different coordinate of (x,y) for y=3x.

x-Coordinate y-Coordinate (x,y) Coordinate
0 0 (0,0)
1 3 (1,3)

The graph of region R: z=0,y=0,y=3x,x=1,

For order of limit, the bounds for x are 0≤x≤1 and bounds for y are 0≤y≤3x.

The volume for the solid region is,

Volume=∫01∫03x(1x2+4)dydx

For order of limit the bounds for y are 0≤y≤3 and bounds for x are 0≤x≤y3.

The volume for the solid region is,

Volume=∫03∫0y3(1x2+4)dxdy

Integration is independent from order of limit

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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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, Rochester, New York, averages µ = 2 l .9 inches of snow for the month of December. The distribution of snowfa...

Statistics for The Behavioral Sciences (MindTap Course List)

Evaluate the following limits, if they exist, where x denotes the greatest integer function. (a) limx0xx (b) li...

Single Variable Calculus

48. Seawater pressure In seawater, the pressure p is related to the depth d according to Where d is in feet a...

Mathematical Applications for the Management, Life, and Social Sciences

Evaluate the algebraic expressions in Problems 35-57 for the given values of the variables. Objectives 2 3x+7y,...

Intermediate Algebra

Simplify each expression in Exercises 1730, expressing your answer in positive exponent form. x3x4

Finite Mathematics

A sample of n sludge specimens is selected and the pH of each one is determined. The one-sample t test will the...

Probability and Statistics for Engineering and the Sciences

Exercises 30,31 On the protractor shown for Exercise 30, MNP and PNQ are complementary. Find x.

Elementary Geometry For College Students, 7e

Solve the following word problems. Round dollars to the nearest cent and percents to the nearest tenth of a per...

Contemporary Mathematics for Business & Consumers

24. Show that is a maximal ideal of.

Elements Of Modern Algebra

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

Trigonometry (MindTap Course List)

Solve each inequality and graph its solution on the number line: x24

Elementary Technical Mathematics

Counting Problem In how many different orders can a basketball team win exactly three out of their laslt five g...

Mathematical Excursions (MindTap Course List)

Area and CentroidConsider the region bounded by the x-axis and one arch of the cycloid with parametric equation...

Calculus: Early Transcendental Functions (MindTap Course List)

Finding a Derivative In Exercises 43-66, find the derivative of the function. f(x)=ln3x

Calculus of a Single Variable

Find the most general antiderivative of the function. (Check your answer by differentiation.) f(x)=x3,42x21

Single Variable Calculus: Early Transcendentals

QUALITY CONTROL PAR Bearings is the principal supplier of the balls bearing for the Sperry Gyroscope Company. I...

Finite Mathematics for the Managerial, Life, and Social Sciences

In Exercises 25 to 32, name the type of reasoning if any used. You know the rule If a person lives in the Santa...

Elementary Geometry for College Students

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

Calculus

The quadratic approximation for at a = 1 is:

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Spherical-to-Cylindrical ConversionIn Exercises 6570, convert the point from spherical coordinates to cylindric...

Multivariable Calculus

True or False: is a convergent series.

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

Assume that the test scores from a college admissions test are normally distributed, with amean of 450 and a st...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Describe the disadvantages of a multiple-treatment design, compared to a two-treatment design, for a within-sub...

Research Methods for the Behavioral Sciences (MindTap Course List)

The following graphs appear in the paper Which Thoughts Count? Algorithms for Evaluating Satisfaction in Relati...

Introduction To Statistics And Data Analysis

Decompose each fraction into partial fractions. 4x2+4x-2xx2-1

College Algebra (MindTap Course List)

Solve each of the following equations using the division principle of equality. Check each answer. 24=38D

Mathematics For Machine Technology

Describe the general characteristics of the case study design, identity the different situations for which this...

Research Methods for the Behavioral Sciences (MindTap Course List)

Ten individuals participated in a taste test involving two brands of a product. Sample results show 7 preferred...

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

Determining if a Function Is Homogeneous In Exercises 69-76, determine whether the function is homogeneous. and...

Calculus (MindTap Course List)

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