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

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Chapter 7.8, Problem 22E
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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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Evaluating a Double Integral In Exercises 11-24, evaluate the double integral. See

∫ 0 4 ∫ 0 x 2 x 2 + 1 d y   d x

To determine

To calculate: The double integration ∫04∫0x(2x2+1)dydx.

Explanation

Given Information:

The provided integration is ∫04∫0x(2x2+1)dydx.

Formula used:

If a binary function F(x,y) is integrable in domain of a≤y≤b and c≤x≤d, the double integration ∫cd∫abF(x,y)dydx can be calculated as follows procedure,

Integrate with respect to y by holding x constant,

∫cd∫abF(x,y)dydx=∫cd[f(x,y)]abdx

Here, function f(x,y) is partial integration of F(x,y) with respect to y variable.

Now, replace the y by limit of integration,

∫cd[f(x,y)]abdx=∫cd[f(x,b)−f(x,a)]dx

Integrate with respect to x,

∫cd[f(x,b)−f(x,a)]dx=[h(x,b)−h(x,a)]cd

Here, the function h(x,b) and is partial integration of f(x,b) with respect to x variable, the function h(x,a) is partial integration of f(x,a) with respect to x variable.

Now, replace the x by limit of integration,

[h(x,b)−h(x,a)]cd=[h(d,b)−h(c,b)−h(d,a)+h(c,a)]

The double integration ∫cd∫abF(x,y)dydx is [h(d,b)−h(c,b)−h(d,a)+h(c,a)]

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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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A sample is selected from a population with a mean of =40 and a standard deviation of =8 . If the sample has n=...

Statistics for The Behavioral Sciences (MindTap Course List)

Suppose f and g are continuous functions such that g(2) = 6 and limx2 [3f(x) + f(x)g(x)] = 36. Find f(2).

Single Variable Calculus

The calibration of a scale is to be checked by weighing a 10-kg test specimen 25 times. Suppose that the result...

Probability and Statistics for Engineering and the Sciences

Let a=log2,b=log3, and c=log7. In Exercises 2946, use the logarithm identities to express the given quantity in...

Finite Mathematics

For Problems 64-78, translate each English phrase into an algebraic expression and use n to represent the unkno...

Intermediate Algebra

Present value If an investment has a goal (future value) of $S after years. Invested at interest rate (as deci...

Mathematical Applications for the Management, Life, and Social Sciences

Binets Formula The following formula is known as Binet's formula for the nth Fibonacci number. Fn=15[ (1+52)n(1...

Mathematical Excursions (MindTap Course List)

Two cars start moving from the same point. One travels south at60 mi/h and the other travels west at 25 mi/h. A...

Single Variable Calculus: Early Transcendentals

Prove that each of the following identities is true. sin4Acos4A=12cos2A

Trigonometry (MindTap Course List)

Change each hexadecimal number to decimal form: D3

Elementary Technical Mathematics

Use the Tax Table, Exhibit 18-3, to calculate the tax liability for the following taxpayers earning under $100,...

Contemporary Mathematics for Business & Consumers

The state of Nevada approximates the shape of a trapezoid with these dimensions for boundaries: 340 miles on th...

Elementary Geometry For College Students, 7e

Exercises Describe the elements in the group of symmetries of the given bounded figure.

Elements Of Modern Algebra

Finding the Limit of a Sequence In Exercises 2124, find the limit of the sequence with the given n th term. an=...

Calculus of a Single Variable

Slant Asymptotes In Exercises 105 and 106, the graph of the function has two slant asymptotes. Identify each sl...

Calculus: Early Transcendental Functions (MindTap Course List)

In Exercises 9 to 28, use the drawings as needed to answer the following questions. Give the meanings of CD,CD,...

Elementary Geometry for College Students

Prove the idempotent law for conjunction, ppp.

Finite Mathematics for the Managerial, Life, and Social Sciences

True or False? In Exercises 6163, determine whether the statement is true or false. If it is false, explain why...

Multivariable Calculus

Find the Jacobian for x = u2v2, y = u2 + v2. 2uv3 − 2u3v 4u2v − 4uv2 2u2v − 2uv2 4uv3 − 4u3v

Study Guide for Stewart's Multivariable Calculus, 8th

Finding the Volume of a Solid In Exercises 912, write and evaluate the definite integral that represents the vo...

Calculus

Using the Second Partials TestIn Exercises 924, find all relative extrema and saddle points of the function. Us...

Calculus (MindTap Course List)

f(x) = x3 2x2 + x 1 has a local maximum at: a) 0 b) 1 c) 13 d) f has no local maxima

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

Corporate triple-A bond interest rates for 12 consecutive months follow. 9.59.39.49.69.89.79.810.59.99.79.69.6 ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Describe quota sampling, recognize examples of this technique in research reports, and explain why it is used.

Research Methods for the Behavioral Sciences (MindTap Course List)

For each of the values in the following table, the true value and measured value are given. Determine the absol...

Mathematics For Machine Technology

Distinguish between science and pseudoscience.

Research Methods for the Behavioral Sciences (MindTap Course List)

Consider the scatterplot of acrylamide concentration versus frying time from the previous exercise. a. Which ob...

Introduction To Statistics And Data Analysis

Let the function f be defined by y=fx, where x and fx are real numbers. Find f2, f-3, fk, and fk2-1. fx=x3-1

College Algebra (MindTap Course List)

In Exercises 1-14, find the future value of the given annuity. Ordinary annuity, 175 monthly payment, 618 inter...

Mathematics: A Practical Odyssey

In 2011, home prices and mortgage rates fell so far that in a number of cities the monthly cost of owning a hom...

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

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