Explanation Given information: The provided integral is: ∫ − ∞ 0 2 x x 2 − 1 d x Formula used: Improper integral with an infinite limit of integration : ∫ a b f ( x ) d x = lim r → 0 − ∫ a 0 f ( x ) d x + lim r → 0 + ∫ 0 b f ( x ) d x Provide that the limit exists. If the limit exists, then ∫ a b f ( x ) d x converges. Otherwise, ∫ a b f ( x ) d x diverges. Calculation: Consider the provided integral is ∫ − ∞ 0 2 x x 2 − 1 d x . Consider the formula, ∫ a b f ( x ) d x = ∫ a c f ( x ) d x + ∫ c b f ( x ) d x Substituting 2 x x 2 − 1 for f ( x ) , − ∞ for a , 0 for b and − 1 for c in above formula to get, ∫ − ∞ 0 2 x x 2 − 1 d x = ∫ − ∞ − 1 2 x x 2 − 1 d x + ∫ − 1 0 2 x x 2 − 1 d x Solving second part of the given integral as, ∫ 0 1 2 x x 2 − 1 d x = lim r → 0 + ∫ − 1 0 2 x x 2 − 1 d x Let, u = x 2 − 1

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 14.5, Problem 26E

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To calculate: The integral ∫−∞02xx2−1dx if it converges.

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Chapter 14.5, Problem 25E

Chapter 14.5, Problem 27E

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Chapter 14 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

Ch. 14.1 - In Exercises 140, evaluate the integral using...Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E Ch. 14.1 - Prob. 6E Ch. 14.1 - Prob. 7E Ch. 14.1 - Prob. 8E Ch. 14.1 - Prob. 9E Ch. 14.1 - Prob. 10E

Ch. 14.1 - Prob. 11E Ch. 14.1 - In Exercises 140, evaluate the integral using...Ch. 14.1 - Prob. 13E Ch. 14.1 - Prob. 14E Ch. 14.1 - Prob. 15E Ch. 14.1 - Prob. 16E Ch. 14.1 - Prob. 17E Ch. 14.1 - Prob. 18E Ch. 14.1 - Prob. 19E Ch. 14.1 - Prob. 20E Ch. 14.1 - Prob. 21E Ch. 14.1 - Prob. 22E Ch. 14.1 - Prob. 23E Ch. 14.1 - Prob. 24E Ch. 14.1 - In Exercises 140, evaluate the integral using...Ch. 14.1 - Prob. 26E Ch. 14.1 - Prob. 27E Ch. 14.1 - Prob. 28E Ch. 14.1 - Prob. 29E Ch. 14.1 - Prob. 30E Ch. 14.1 - Prob. 31E Ch. 14.1 - Prob. 32E Ch. 14.1 - Prob. 33E Ch. 14.1 - Prob. 34E Ch. 14.1 - Prob. 35E Ch. 14.1 - Prob. 36E Ch. 14.1 - In Exercises 140, evaluate the integral using...Ch. 14.1 - In Exercises 140, evaluate the integral using...Ch. 14.1 - In Exercises 140, evaluate the integral using...Ch. 14.1 - Prob. 40E Ch. 14.1 - Prob. 41E Ch. 14.1 - Prob. 42E Ch. 14.1 - Prob. 43E Ch. 14.1 - Prob. 44E Ch. 14.1 - Prob. 45E Ch. 14.1 - Prob. 46E Ch. 14.1 - Prob. 47E Ch. 14.1 - Prob. 48E Ch. 14.1 - Prob. 49E Ch. 14.1 - Prob. 50E Ch. 14.1 - Prob. 51E Ch. 14.1 - Prob. 52E Ch. 14.1 - Prob. 53E Ch. 14.1 - Prob. 54E Ch. 14.1 - Prob. 55E Ch. 14.1 - Prob. 56E Ch. 14.1 - Spending on Gasoline From the beginning of 2000 to...Ch. 14.1 - Spending on Gasoline From the beginning of 2007 to...Ch. 14.1 - Housing The following graph shows the annual...Ch. 14.1 - Housing for Sale The following graph shows the...Ch. 14.1 - Prob. 61E Ch. 14.1 - Bottled Water Sales The rate of U.S. sales of...Ch. 14.1 - Oil Production in Mexico The rate of crude oil...Ch. 14.1 - Oil Imports from Mexico The rate of crude oil...Ch. 14.1 - Prob. 65E Ch. 14.1 - Prob. 66E Ch. 14.1 - Prob. 67E Ch. 14.1 - Integrals of Piecewise-Linear Functions Exercises...Ch. 14.1 - Prob. 69E Ch. 14.1 - Prob. 70E Ch. 14.1 - Prob. 71E Ch. 14.1 - Prob. 72E Ch. 14.1 - Prob. 73E Ch. 14.1 - Prob. 74E Ch. 14.1 - In Exercises 7380, indicate whether the given...Ch. 14.1 - Prob. 76E Ch. 14.1 - Prob. 77E Ch. 14.1 - Prob. 78E Ch. 14.1 - Prob. 79E Ch. 14.1 - Prob. 80E Ch. 14.1 - Prob. 81E Ch. 14.1 - Prob. 82E Ch. 14.1 - Prob. 83E Ch. 14.1 - Prob. 84E Ch. 14.2 - In Exercises 18, find the area of the shaded...Ch. 14.2 - Prob. 2E Ch. 14.2 - Prob. 3E Ch. 14.2 - Prob. 4E Ch. 14.2 - Prob. 5E Ch. 14.2 - Prob. 6E Ch. 14.2 - Prob. 7E Ch. 14.2 - Prob. 8E Ch. 14.2 - Prob. 9E Ch. 14.2 - Prob. 10E Ch. 14.2 - Prob. 11E Ch. 14.2 - Prob. 12E Ch. 14.2 - Prob. 13E Ch. 14.2 - Prob. 14E Ch. 14.2 - Prob. 15E Ch. 14.2 - Prob. 16E Ch. 14.2 - Prob. 17E Ch. 14.2 - Prob. 18E Ch. 14.2 - Prob. 19E Ch. 14.2 - Prob. 20E Ch. 14.2 - Prob. 21E Ch. 14.2 - Prob. 22E Ch. 14.2 - Prob. 23E Ch. 14.2 - Prob. 24E Ch. 14.2 - Prob. 25E Ch. 14.2 - In Exercises 942, find the area of the indicated...Ch. 14.2 - Prob. 27E Ch. 14.2 - Prob. 28E Ch. 14.2 - Prob. 29E Ch. 14.2 - Prob. 30E Ch. 14.2 - Prob. 31E Ch. 14.2 - Prob. 32E Ch. 14.2 - Prob. 33E Ch. 14.2 - Prob. 34E Ch. 14.2 - Prob. 35E Ch. 14.2 - Prob. 36E Ch. 14.2 - Prob. 37E Ch. 14.2 - Prob. 38E Ch. 14.2 - Prob. 39E Ch. 14.2 - Prob. 40E Ch. 14.2 - Prob. 41E Ch. 14.2 - In Exercises 942, find the area of the indicated...Ch. 14.2 - Prob. 43E Ch. 14.2 - Prob. 44E Ch. 14.2 - Prob. 45E Ch. 14.2 - Oil Production in Mexico: Pemex The rate of crude...Ch. 14.2 - Prob. 47E Ch. 14.2 - Prob. 48E Ch. 14.2 - Prob. 49E Ch. 14.2 - Prob. 50E Ch. 14.2 - Prob. 51E Ch. 14.2 - Prob. 52E Ch. 14.2 - Prob. 53E Ch. 14.2 - Prob. 54E Ch. 14.2 - Prob. 55E Ch. 14.2 - Prob. 56E Ch. 14.2 - Prob. 57E Ch. 14.2 - Prob. 58E Ch. 14.3 - Prob. 1E Ch. 14.3 - Prob. 2E Ch. 14.3 - Prob. 3E Ch. 14.3 - Prob. 4E Ch. 14.3 - Prob. 5E Ch. 14.3 - Prob. 6E Ch. 14.3 - Prob. 7E Ch. 14.3 - Prob. 8E Ch. 14.3 - Prob. 9E Ch. 14.3 - Prob. 10E Ch. 14.3 - In Exercises 11 and 12, some values of a function...Ch. 14.3 - Prob. 12E Ch. 14.3 - Prob. 13E Ch. 14.3 - Prob. 14E Ch. 14.3 - Prob. 15E Ch. 14.3 - Prob. 16E Ch. 14.3 - Prob. 17E Ch. 14.3 - Prob. 18E Ch. 14.3 - Prob. 19E Ch. 14.3 - Prob. 20E Ch. 14.3 - In Exercises 1324, calculate the 5-unit moving...Ch. 14.3 - Prob. 22E Ch. 14.3 - Prob. 23E Ch. 14.3 - Prob. 24E Ch. 14.3 - Prob. 25E Ch. 14.3 - Prob. 26E Ch. 14.3 - Prob. 27E Ch. 14.3 - Prob. 28E Ch. 14.3 - Prob. 29E Ch. 14.3 - Prob. 30E Ch. 14.3 - Prob. 31E Ch. 14.3 - Prob. 32E Ch. 14.3 - Prob. 33E Ch. 14.3 - Prob. 34E Ch. 14.3 - Television Advertising The cost, in millions of...Ch. 14.3 - Television Advertising The cost, in millions of...Ch. 14.3 - Prob. 37E Ch. 14.3 - Prob. 38E Ch. 14.3 - Prob. 39E Ch. 14.3 - Health Expenditures Annual expenditures on health...Ch. 14.3 - Prob. 41E Ch. 14.3 - Prob. 42E Ch. 14.3 - Prob. 43E Ch. 14.3 - Prob. 44E Ch. 14.3 - Prob. 45E Ch. 14.3 - Prob. 46E Ch. 14.3 - Prob. 47E Ch. 14.3 - Prob. 48E Ch. 14.3 - Prob. 49E Ch. 14.3 - Prob. 50E Ch. 14.3 - Prob. 51E Ch. 14.3 - Prob. 52E Ch. 14.3 - Prob. 53E Ch. 14.3 - Prob. 54E Ch. 14.3 - Prob. 55E Ch. 14.3 - Pasta Imports in the 1990s In 1990 the United...Ch. 14.3 - Prob. 57E Ch. 14.3 - Prob. 58E Ch. 14.3 - Prob. 59E Ch. 14.3 - Prob. 60E Ch. 14.3 - Prob. 61E Ch. 14.3 - Prob. 62E Ch. 14.3 - Prob. 63E Ch. 14.3 - Prob. 64E Ch. 14.3 - Prob. 65E Ch. 14.3 - Prob. 66E Ch. 14.3 - Prob. 67E Ch. 14.3 - Prob. 68E Ch. 14.4 - In Exercises 112, calculate the consumers surplus...Ch. 14.4 - Prob. 2E Ch. 14.4 - Prob. 3E Ch. 14.4 - Prob. 4E Ch. 14.4 - Prob. 5E Ch. 14.4 - Prob. 6E Ch. 14.4 - Prob. 7E Ch. 14.4 - Prob. 8E Ch. 14.4 - Prob. 9E Ch. 14.4 - In Exercises 112, calculate the consumers surplus...Ch. 14.4 - Prob. 11E Ch. 14.4 - Prob. 12E Ch. 14.4 - Prob. 13E Ch. 14.4 - Prob. 14E Ch. 14.4 - Prob. 15E Ch. 14.4 - Prob. 16E Ch. 14.4 - Prob. 17E Ch. 14.4 - Prob. 18E Ch. 14.4 - Prob. 19E Ch. 14.4 - In Exercises 1324, calculate the producers surplus...Ch. 14.4 - Prob. 21E Ch. 14.4 - Prob. 22E Ch. 14.4 - Prob. 23E Ch. 14.4 - Prob. 24E Ch. 14.4 - Prob. 25E Ch. 14.4 - Prob. 26E Ch. 14.4 - Prob. 27E Ch. 14.4 - Prob. 28E Ch. 14.4 - Prob. 29E Ch. 14.4 - Prob. 30E Ch. 14.4 - Prob. 31E Ch. 14.4 - Prob. 32E Ch. 14.4 - In Exercises 3136, find the total value of the...Ch. 14.4 - Prob. 34E Ch. 14.4 - Prob. 35E Ch. 14.4 - Prob. 36E Ch. 14.4 - Prob. 37E Ch. 14.4 - Fast Food A fast-food outlet finds that the demand...Ch. 14.4 - Prob. 39E Ch. 14.4 - Prob. 40E Ch. 14.4 - Revenue: Walmart The annual revenue earned by...Ch. 14.4 - Prob. 42E Ch. 14.4 - Prob. 43E Ch. 14.4 - Prob. 44E Ch. 14.4 - Prob. 45E Ch. 14.4 - Prob. 46E Ch. 14.4 - Prob. 47E Ch. 14.4 - Saving for College When your first child is born,...Ch. 14.4 - Prob. 49E Ch. 14.4 - Prob. 50E Ch. 14.4 - Prob. 51E Ch. 14.4 - Prob. 52E Ch. 14.4 - Valuing Future Income Inga was injured and can no...Ch. 14.4 - Prob. 54E Ch. 14.4 - Prob. 55E Ch. 14.4 - Prob. 56E Ch. 14.4 - Prob. 57E Ch. 14.4 - Prob. 58E Ch. 14.4 - Prob. 59E Ch. 14.4 - Prob. 60E Ch. 14.4 - Prob. 61E Ch. 14.4 - Prob. 62E Ch. 14.5 - In Exercises 126, decide whether or not the given...Ch. 14.5 - Prob. 2E Ch. 14.5 - Prob. 3E Ch. 14.5 - Prob. 4E Ch. 14.5 - Prob. 5E Ch. 14.5 - Prob. 6E Ch. 14.5 - Prob. 7E Ch. 14.5 - Prob. 8E Ch. 14.5 - Prob. 9E Ch. 14.5 - Prob. 10E Ch. 14.5 - Prob. 11E Ch. 14.5 - Prob. 12E Ch. 14.5 - Prob. 13E Ch. 14.5 - Prob. 14E Ch. 14.5 - Prob. 15E Ch. 14.5 - Prob. 16E Ch. 14.5 - Prob. 17E Ch. 14.5 - Prob. 18E Ch. 14.5 - Prob. 19E Ch. 14.5 - Prob. 20E Ch. 14.5 - Prob. 21E Ch. 14.5 - Prob. 22E Ch. 14.5 - Prob. 23E Ch. 14.5 - Prob. 24E Ch. 14.5 - Prob. 25E Ch. 14.5 - Prob. 26E Ch. 14.5 - Prob. 27E Ch. 14.5 - Prob. 28E Ch. 14.5 - Prob. 29E Ch. 14.5 - Prob. 30E Ch. 14.5 - Prob. 31E Ch. 14.5 - Prob. 32E Ch. 14.5 - Prob. 33E Ch. 14.5 - Prob. 34E Ch. 14.5 - Prob. 35E Ch. 14.5 - Revenue from New Home Sales Revenue from the sale...Ch. 14.5 - Prob. 37E Ch. 14.5 - Prob. 38E Ch. 14.5 - Prob. 39E Ch. 14.5 - Prob. 40E Ch. 14.5 - Prob. 41E Ch. 14.5 - Prob. 42E Ch. 14.5 - Prob. 43E Ch. 14.5 - Prob. 44E Ch. 14.5 - Prob. 45E Ch. 14.5 - Prob. 46E Ch. 14.5 - Prob. 47E Ch. 14.5 - Prob. 48E Ch. 14.5 - Prob. 49E Ch. 14.5 - Prob. 50E Ch. 14.5 - Prob. 51E Ch. 14.5 - Prob. 52E Ch. 14.5 - Prob. 53E Ch. 14.5 - Prob. 54E Ch. 14.5 - Prob. 55E Ch. 14.5 - Meteor Impacts (continuing Exercise 55.) a....Ch. 14.5 - Prob. 57E Ch. 14.5 - Prob. 58E Ch. 14.5 - Prob. 59E Ch. 14.5 - Prob. 60E Ch. 14.5 - Prob. 61E Ch. 14.5 - Prob. 62E Ch. 14.5 - Prob. 63E Ch. 14.5 - Prob. 64E Ch. 14.5 - Prob. 65E Ch. 14.6 - Prob. 1E Ch. 14.6 - Prob. 2E Ch. 14.6 - In Exercises 1-10, find the general solution of...Ch. 14.6 - Prob. 4E Ch. 14.6 - Prob. 5E Ch. 14.6 - Prob. 6E Ch. 14.6 - Prob. 7E Ch. 14.6 - Prob. 8E Ch. 14.6 - Prob. 9E Ch. 14.6 - Prob. 10E Ch. 14.6 - Prob. 11E Ch. 14.6 - Prob. 12E Ch. 14.6 - Prob. 13E Ch. 14.6 - Prob. 14E Ch. 14.6 - Prob. 15E Ch. 14.6 - Prob. 16E Ch. 14.6 - Prob. 17E Ch. 14.6 - Prob. 18E Ch. 14.6 - Prob. 19E Ch. 14.6 - Prob. 20E Ch. 14.6 - Prob. 21E Ch. 14.6 - Prob. 22E Ch. 14.6 - Prob. 23E Ch. 14.6 - Newtons Law of Cooling For coffee in a paper cup,...Ch. 14.6 - Prob. 25E Ch. 14.6 - Prob. 26E Ch. 14.6 - Prob. 27E Ch. 14.6 - Prob. 28E Ch. 14.6 - Determining Demand Nancys Chocolates estimates...Ch. 14.6 - Prob. 30E Ch. 14.6 - Prob. 31E Ch. 14.6 - Prob. 32E Ch. 14.6 - Prob. 33E Ch. 14.6 - Prob. 34E Ch. 14.6 - Prob. 35E Ch. 14.6 - Prob. 36E Ch. 14.6 - Prob. 37E Ch. 14.6 - Prob. 38E Ch. 14.6 - Prob. 39E Ch. 14.6 - Prob. 40E Ch. 14.6 - Prob. 41E Ch. 14.6 - Prob. 42E Ch. 14.6 - Exercises 4144 require the use of technology....Ch. 14.6 - Prob. 44E Ch. 14.6 - Prob. 45E Ch. 14.6 - Prob. 46E Ch. 14.6 - Prob. 47E Ch. 14.6 - Prob. 48E Ch. 14.6 - Prob. 49E Ch. 14.6 - Prob. 50E Ch. 14 - Prob. 1RE Ch. 14 - Prob. 2RE Ch. 14 - Prob. 3RE Ch. 14 - In Exercises 1-10, evaluate the given integral....Ch. 14 - Prob. 5RE Ch. 14 - Prob. 6RE Ch. 14 - Prob. 7RE Ch. 14 - Prob. 8RE Ch. 14 - Prob. 9RE Ch. 14 - Prob. 10RE Ch. 14 - Prob. 11RE Ch. 14 - Prob. 12RE Ch. 14 - Prob. 13RE Ch. 14 - Prob. 14RE Ch. 14 - Prob. 15RE Ch. 14 - Prob. 16RE Ch. 14 - Prob. 17RE Ch. 14 - Prob. 18RE Ch. 14 - Prob. 19RE Ch. 14 - Prob. 20RE Ch. 14 - Prob. 21RE Ch. 14 - Prob. 22RE Ch. 14 - Prob. 23RE Ch. 14 - Prob. 24RE Ch. 14 - Prob. 25RE Ch. 14 - Prob. 26RE Ch. 14 - Prob. 27RE Ch. 14 - Prob. 28RE Ch. 14 - Prob. 29RE Ch. 14 - In Exercises 27-32, decide whether the given...Ch. 14 - Prob. 31RE Ch. 14 - Prob. 32RE Ch. 14 - Prob. 33RE Ch. 14 - Prob. 34RE Ch. 14 - Prob. 35RE Ch. 14 - Prob. 36RE Ch. 14 - Prob. 37RE Ch. 14 - Spending on Shipping During the past 10 months,...Ch. 14 - Prob. 39RE Ch. 14 - Investments OHaganBooks.com keeps its cash...Ch. 14 - Prob. 41RE Ch. 14 - Prob. 42RE Ch. 14 - Prob. 43RE Ch. 14 - Prob. 44RE Ch. 14 - Prob. 45RE Ch. 14 - Prob. 46RE Ch. 14 - Acquisitions The Megabucks Corporation is...Ch. 14 - Prob. 48RE Ch. 14 - Prob. 49RE Ch. 14 - Prob. 50RE

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The integral ∫ − ∞ 0 2 x x 2 − 1 d x if it converges.

Solution Summary: The author calculates the integral displaystyle 'underset-infty' if it converges. If the limit exists, it diverges.

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To calculate: The integral ∫−∞02xx2−1dx if it converges.

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Chapter 14 Solutions