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Math Calculus Finite Mathematics and Applied Calculus (MindTap Course List)

To prove: That the substitutions u = − x , u = x 2 and u = − x 2 are not useful for the integral ∫ e − x 2 d x .

To prove: That the substitutions u = − x , u = x 2 and u = − x 2 are not useful for the integral ∫ e − x 2 d x .

Solution Summary: The author explains how to solve an integral using substitution rule.

Finite Mathematics and Applied Calculus (MindTap Course List)

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 13.2, Problem 109E

To determine

To prove: That the substitutions u=−x, u=x2 and u=−x2 are not useful for the integral ∫e−x2dx.

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Chapter 13.2, Problem 108E

Chapter 13.2, Problem 110E

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Chapter 13 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

Ch. 13.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

Ch. 13.1 - Prob. 11E Ch. 13.1 - Prob. 12E Ch. 13.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 13.1 - Prob. 14E Ch. 13.1 - Prob. 15E Ch. 13.1 - Prob. 16E Ch. 13.1 - Prob. 17E Ch. 13.1 - Prob. 18E Ch. 13.1 - Prob. 19E Ch. 13.1 - Prob. 20E Ch. 13.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 13.1 - Prob. 22E Ch. 13.1 - Prob. 23E Ch. 13.1 - Prob. 24E Ch. 13.1 - Prob. 25E Ch. 13.1 - Prob. 26E Ch. 13.1 - Prob. 27E Ch. 13.1 - Prob. 28E Ch. 13.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 13.1 - Prob. 30E Ch. 13.1 - Prob. 31E Ch. 13.1 - Prob. 32E Ch. 13.1 - Prob. 33E Ch. 13.1 - Prob. 34E Ch. 13.1 - Prob. 35E Ch. 13.1 - Prob. 36E Ch. 13.1 - Prob. 37E Ch. 13.1 - Prob. 38E Ch. 13.1 - Prob. 39E Ch. 13.1 - Prob. 40E Ch. 13.1 - Prob. 41E Ch. 13.1 - Prob. 42E Ch. 13.1 - Prob. 43E Ch. 13.1 - Prob. 44E Ch. 13.1 - Prob. 45E Ch. 13.1 - Prob. 46E Ch. 13.1 - Prob. 47E Ch. 13.1 - Prob. 48E Ch. 13.1 - Prob. 49E Ch. 13.1 - Prob. 50E Ch. 13.1 - Facebook Membership At the start of 2010, Facebook...Ch. 13.1 - Prob. 52E Ch. 13.1 - Median Household Income From 2000 to 2007, median...Ch. 13.1 - Prob. 54E Ch. 13.1 - Prob. 55E Ch. 13.1 - Bottled Water Sales The rate of U.S. per capita...Ch. 13.1 - Prob. 57E Ch. 13.1 - Health-Care Spending in the 2000s Write H(t) for...Ch. 13.1 - Prob. 59E Ch. 13.1 - Prob. 60E Ch. 13.1 - Prob. 61E Ch. 13.1 - Prob. 62E Ch. 13.1 - Prob. 63E Ch. 13.1 - Prob. 64E Ch. 13.1 - Vertical Motion under Gravity Your name is Galileo...Ch. 13.1 - Prob. 66E Ch. 13.1 - Prob. 67E Ch. 13.1 - Prob. 68E Ch. 13.1 - Prob. 69E Ch. 13.1 - Prob. 70E Ch. 13.1 - Prob. 71E Ch. 13.1 - Prob. 72E Ch. 13.1 - Exercises 7176 use the results of Exercises 69 and...Ch. 13.1 - Prob. 74E Ch. 13.1 - Prob. 75E Ch. 13.1 - Prob. 76E Ch. 13.1 - Prob. 77E Ch. 13.1 - Prob. 78E Ch. 13.1 - Prob. 79E Ch. 13.1 - Prob. 80E Ch. 13.1 - Prob. 81E Ch. 13.1 - Prob. 82E Ch. 13.1 - Prob. 83E Ch. 13.1 - Prob. 84E Ch. 13.1 - Prob. 85E Ch. 13.1 - Prob. 86E Ch. 13.1 - Prob. 87E Ch. 13.1 - Prob. 88E Ch. 13.1 - Prob. 89E Ch. 13.1 - Prob. 90E Ch. 13.1 - Prob. 91E Ch. 13.1 - Prob. 92E Ch. 13.1 - Prob. 93E Ch. 13.1 - Prob. 94E Ch. 13.1 - Why was the following marked wrong? How should it...Ch. 13.1 - Prob. 96E Ch. 13.1 - Prob. 97E Ch. 13.1 - Prob. 98E Ch. 13.1 - Prob. 99E Ch. 13.1 - Prob. 100E Ch. 13.1 - Prob. 101E Ch. 13.1 - Prob. 102E Ch. 13.2 - In Exercises 110, evaluate the given integral...Ch. 13.2 - In Exercises 110, evaluate the given integral...Ch. 13.2 - Prob. 3E Ch. 13.2 - Prob. 4E Ch. 13.2 - Prob. 5E Ch. 13.2 - Prob. 6E Ch. 13.2 - Prob. 7E Ch. 13.2 - Prob. 8E Ch. 13.2 - Prob. 9E Ch. 13.2 - Prob. 10E Ch. 13.2 - Prob. 11E Ch. 13.2 - Prob. 12E Ch. 13.2 - Prob. 13E Ch. 13.2 - Prob. 14E Ch. 13.2 - Prob. 15E Ch. 13.2 - Prob. 16E Ch. 13.2 - Prob. 17E Ch. 13.2 - Prob. 18E Ch. 13.2 - Prob. 19E Ch. 13.2 - Prob. 20E Ch. 13.2 - Prob. 21E Ch. 13.2 - Prob. 22E Ch. 13.2 - Prob. 23E Ch. 13.2 - Prob. 24E Ch. 13.2 - Prob. 25E Ch. 13.2 - Prob. 26E Ch. 13.2 - Prob. 27E Ch. 13.2 - Prob. 28E Ch. 13.2 - Prob. 29E Ch. 13.2 - Prob. 30E Ch. 13.2 - Prob. 31E Ch. 13.2 - Prob. 32E Ch. 13.2 - Prob. 33E Ch. 13.2 - Prob. 34E Ch. 13.2 - Prob. 35E Ch. 13.2 - Prob. 36E Ch. 13.2 - Prob. 37E Ch. 13.2 - Prob. 38E Ch. 13.2 - Prob. 39E Ch. 13.2 - Prob. 40E Ch. 13.2 - Prob. 41E Ch. 13.2 - Prob. 42E Ch. 13.2 - Prob. 43E Ch. 13.2 - Prob. 44E Ch. 13.2 - Prob. 45E Ch. 13.2 - Prob. 46E Ch. 13.2 - Prob. 47E Ch. 13.2 - Prob. 48E Ch. 13.2 - Prob. 49E Ch. 13.2 - Prob. 50E Ch. 13.2 - Prob. 51E Ch. 13.2 - Prob. 52E Ch. 13.2 - Prob. 53E Ch. 13.2 - Prob. 54E Ch. 13.2 - Prob. 55E Ch. 13.2 - In Exercises 5356, derive the given equation,...Ch. 13.2 - Prob. 57E Ch. 13.2 - Prob. 58E Ch. 13.2 - Prob. 59E Ch. 13.2 - Prob. 60E Ch. 13.2 - Prob. 61E Ch. 13.2 - Prob. 62E Ch. 13.2 - Prob. 63E Ch. 13.2 - Prob. 64E Ch. 13.2 - Prob. 65E Ch. 13.2 - Prob. 66E Ch. 13.2 - Prob. 67E Ch. 13.2 - Prob. 68E Ch. 13.2 - Prob. 69E Ch. 13.2 - Prob. 70E Ch. 13.2 - Prob. 71E Ch. 13.2 - Prob. 72E Ch. 13.2 - Prob. 73E Ch. 13.2 - Prob. 74E Ch. 13.2 - Prob. 75E Ch. 13.2 - Prob. 76E Ch. 13.2 - Prob. 77E Ch. 13.2 - Prob. 78E Ch. 13.2 - In Exercises 7784, use Mikes shortcut method (see...Ch. 13.2 - In Exercises 7784, use Mikes shortcut method (see...Ch. 13.2 - In Exercises 7784, use Mikes shortcut method (see...Ch. 13.2 - Prob. 82E Ch. 13.2 - Prob. 83E Ch. 13.2 - Prob. 84E Ch. 13.2 - Cost The marginal cost of producing the xth roll...Ch. 13.2 - Prob. 86E Ch. 13.2 - Economic Growth The Mexico GDP (total monetary...Ch. 13.2 - Housing Starts: The Great Recession The Great...Ch. 13.2 - Revenue: Pacific Sunwear The annual revenue of...Ch. 13.2 - Revenue: Google The annual revenue of Google Inc....Ch. 13.2 - Scientific Research: 19832003 The number of...Ch. 13.2 - Scientific Research: 19832003 The number of...Ch. 13.2 - Sales The rate of sales of your companys Jackson...Ch. 13.2 - Prob. 94E Ch. 13.2 - Prob. 95E Ch. 13.2 - Prob. 96E Ch. 13.2 - Bottled Water Sales (Compare Exercise 55 in...Ch. 13.2 - Prob. 98E Ch. 13.2 - Prob. 99E Ch. 13.2 - Prob. 100E Ch. 13.2 - Prob. 101E Ch. 13.2 - Prob. 102E Ch. 13.2 - Prob. 103E Ch. 13.2 - Prob. 104E Ch. 13.2 - Prob. 105E Ch. 13.2 - Prob. 106E Ch. 13.2 - Prob. 107E Ch. 13.2 - Prob. 108E Ch. 13.2 - Prob. 109E Ch. 13.2 - Prob. 110E Ch. 13.3 - In Exercises 1-10, calculate the left Riemann sum...Ch. 13.3 - Prob. 2E Ch. 13.3 - Prob. 3E Ch. 13.3 - Prob. 4E Ch. 13.3 - Prob. 5E Ch. 13.3 - Prob. 6E Ch. 13.3 - Prob. 7E Ch. 13.3 - Prob. 8E Ch. 13.3 - Prob. 9E Ch. 13.3 - Prob. 10E Ch. 13.3 - Prob. 11E Ch. 13.3 - Prob. 12E Ch. 13.3 - Prob. 13E Ch. 13.3 - In Exercises 11-18, use the given graph to...Ch. 13.3 - Prob. 15E Ch. 13.3 - In Exercises 11-18, use the given graph to...Ch. 13.3 - Prob. 17E Ch. 13.3 - Prob. 18E Ch. 13.3 - Prob. 19E Ch. 13.3 - Prob. 20E Ch. 13.3 - Prob. 21E Ch. 13.3 - Prob. 22E Ch. 13.3 - Prob. 23E Ch. 13.3 - Prob. 24E Ch. 13.3 - Prob. 25E Ch. 13.3 - Prob. 26E Ch. 13.3 - Prob. 27E Ch. 13.3 - Prob. 28E Ch. 13.3 - Prob. 29E Ch. 13.3 - Prob. 30E Ch. 13.3 - Prob. 31E Ch. 13.3 - In Exercises 29-34, the graph of the derivative...Ch. 13.3 - Prob. 33E Ch. 13.3 - In Exercises 29-34, the graph of the derivative...Ch. 13.3 - Prob. 35E Ch. 13.3 - Prob. 36E Ch. 13.3 - Prob. 37E Ch. 13.3 - Prob. 38E Ch. 13.3 - Prob. 39E Ch. 13.3 - Prob. 40E Ch. 13.3 - Prob. 41E Ch. 13.3 - Cost Repeat Exercise 41 using the marginal cost...Ch. 13.3 - Prob. 43E Ch. 13.3 - Prob. 44E Ch. 13.3 - Prob. 45E Ch. 13.3 - Bottled Water Sales The rate of U.S. per capita...Ch. 13.3 - Prob. 47E Ch. 13.3 - Online Auctions The following graph shows the rate...Ch. 13.3 - Scientific Research Exercises 49 and 50 are based...Ch. 13.3 - Prob. 50E Ch. 13.3 - Graduate Degrees: Women The following graph shows...Ch. 13.3 - Prob. 52E Ch. 13.3 - Prob. 53E Ch. 13.3 - Prob. 54E Ch. 13.3 - Prob. 55E Ch. 13.3 - Prob. 56E Ch. 13.3 - Prob. 57E Ch. 13.3 - Prob. 58E Ch. 13.3 - Prob. 59E Ch. 13.3 - Prob. 60E Ch. 13.3 - Prob. 61E Ch. 13.3 - Prob. 62E Ch. 13.3 - Prob. 63E Ch. 13.3 - Prob. 64E Ch. 13.3 - Prob. 65E Ch. 13.3 - Prob. 66E Ch. 13.3 - Prob. 67E Ch. 13.3 - Prob. 68E Ch. 13.3 - Prob. 69E Ch. 13.3 - Prob. 70E Ch. 13.3 - The Normal Curve The normal distribution curve,...Ch. 13.3 - Prob. 72E Ch. 13.3 - Prob. 73E Ch. 13.3 - Prob. 74E Ch. 13.3 - Prob. 75E Ch. 13.3 - Prob. 76E Ch. 13.3 - Prob. 77E Ch. 13.3 - Prob. 78E Ch. 13.3 - Prob. 79E Ch. 13.3 - Prob. 80E Ch. 13.3 - Prob. 81E Ch. 13.3 - Prob. 82E Ch. 13.3 - Your cellphone company charges you c(t)=20t+100...Ch. 13.3 - Prob. 84E Ch. 13.3 - Prob. 85E Ch. 13.3 - Prob. 86E Ch. 13.3 - Prob. 87E Ch. 13.3 - Prob. 88E Ch. 13.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 13.4 - Prob. 2E Ch. 13.4 - Prob. 3E Ch. 13.4 - Prob. 4E Ch. 13.4 - Prob. 5E Ch. 13.4 - Prob. 6E Ch. 13.4 - Prob. 7E Ch. 13.4 - Prob. 8E Ch. 13.4 - Prob. 9E Ch. 13.4 - Prob. 10E Ch. 13.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 13.4 - Prob. 12E Ch. 13.4 - Prob. 13E Ch. 13.4 - Prob. 14E Ch. 13.4 - Prob. 15E Ch. 13.4 - Prob. 16E Ch. 13.4 - Prob. 17E Ch. 13.4 - Prob. 18E Ch. 13.4 - Prob. 19E Ch. 13.4 - Prob. 20E Ch. 13.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 13.4 - Prob. 22E Ch. 13.4 - Prob. 23E Ch. 13.4 - Prob. 24E Ch. 13.4 - Prob. 25E Ch. 13.4 - Prob. 26E Ch. 13.4 - Prob. 27E Ch. 13.4 - Prob. 28E Ch. 13.4 - Prob. 29E Ch. 13.4 - Prob. 30E Ch. 13.4 - Prob. 31E Ch. 13.4 - Prob. 32E Ch. 13.4 - Prob. 33E Ch. 13.4 - Prob. 34E Ch. 13.4 - Prob. 35E Ch. 13.4 - Prob. 36E Ch. 13.4 - Prob. 37E Ch. 13.4 - Prob. 38E Ch. 13.4 - Prob. 39E Ch. 13.4 - Prob. 40E Ch. 13.4 - Prob. 41E Ch. 13.4 - Prob. 42E Ch. 13.4 - Prob. 43E Ch. 13.4 - Prob. 44E Ch. 13.4 - Prob. 45E Ch. 13.4 - Prob. 46E Ch. 13.4 - Prob. 47E Ch. 13.4 - Prob. 48E Ch. 13.4 - Prob. 49E Ch. 13.4 - Prob. 50E Ch. 13.4 - Prob. 51E Ch. 13.4 - Prob. 52E Ch. 13.4 - Prob. 53E Ch. 13.4 - Prob. 54E Ch. 13.4 - Prob. 55E Ch. 13.4 - Prob. 56E Ch. 13.4 - Prob. 57E Ch. 13.4 - Prob. 58E Ch. 13.4 - Profit: iPhones (Compare Exercise 43 in Section...Ch. 13.4 - Prob. 60E Ch. 13.4 - Prob. 61E Ch. 13.4 - Prob. 62E Ch. 13.4 - Prob. 63E Ch. 13.4 - Prob. 64E Ch. 13.4 - Fuel Consumption The way Professor Waner drives,...Ch. 13.4 - Fuel Consumption The way Professor Costenoble...Ch. 13.4 - Bottled Water Sales (Compare Exercise 45 in...Ch. 13.4 - Bottled Water Sales (Compare Exercise 46 in...Ch. 13.4 - Prob. 69E Ch. 13.4 - Prob. 70E Ch. 13.4 - Prob. 71E Ch. 13.4 - Big Brother (Compare Exercise 66 in Section 13.3.)...Ch. 13.4 - Prob. 73E Ch. 13.4 - Prob. 74E Ch. 13.4 - Prob. 75E Ch. 13.4 - Sales Annual sales of fountain pens in Littleville...Ch. 13.4 - Prob. 77E Ch. 13.4 - Prob. 78E Ch. 13.4 - Prob. 79E Ch. 13.4 - Online Auctions The rate of change n(t) of the...Ch. 13.4 - Prob. 81E Ch. 13.4 - Prob. 82E Ch. 13.4 - Prob. 83E Ch. 13.4 - Prob. 84E Ch. 13.4 - Prob. 85E Ch. 13.4 - Prob. 86E Ch. 13.4 - Prob. 87E Ch. 13.4 - Prob. 88E Ch. 13.4 - Prob. 89E Ch. 13.4 - Prob. 90E Ch. 13.4 - Prob. 91E Ch. 13.4 - Prob. 92E Ch. 13.4 - Prob. 93E Ch. 13.4 - Prob. 94E Ch. 13.4 - Prob. 95E Ch. 13.4 - Prob. 96E Ch. 13.4 - Prob. 97E Ch. 13.4 - Prob. 98E Ch. 13.4 - Prob. 99E Ch. 13.4 - Prob. 100E Ch. 13 - In Exercises 118, evaluate the indefinite...Ch. 13 - Prob. 2RE Ch. 13 - Prob. 3RE Ch. 13 - Prob. 4RE Ch. 13 - Prob. 5RE Ch. 13 - Prob. 6RE Ch. 13 - Prob. 7RE Ch. 13 - Prob. 8RE Ch. 13 - Prob. 9RE Ch. 13 - Prob. 10RE Ch. 13 - Prob. 11RE Ch. 13 - Prob. 12RE Ch. 13 - Prob. 13RE Ch. 13 - Prob. 14RE Ch. 13 - Prob. 15RE Ch. 13 - Prob. 16RE Ch. 13 - Prob. 17RE Ch. 13 - Prob. 18RE Ch. 13 - Prob. 19RE Ch. 13 - Prob. 20RE Ch. 13 - Prob. 21RE Ch. 13 - Prob. 22RE Ch. 13 - In Exercises 2126, calculate the left Riemann sum...Ch. 13 - Prob. 24RE Ch. 13 - Prob. 25RE Ch. 13 - Prob. 26RE Ch. 13 - Prob. 27RE Ch. 13 - Prob. 28RE Ch. 13 - Prob. 29RE Ch. 13 - Prob. 30RE Ch. 13 - Prob. 31RE Ch. 13 - Prob. 32RE Ch. 13 - Prob. 33RE Ch. 13 - Prob. 34RE Ch. 13 - In Exercises 3140, evaluate the definite integral...Ch. 13 - Prob. 36RE Ch. 13 - Prob. 37RE Ch. 13 - Prob. 38RE Ch. 13 - Prob. 39RE Ch. 13 - Prob. 40RE Ch. 13 - Prob. 41RE Ch. 13 - Prob. 42RE Ch. 13 - Prob. 43RE Ch. 13 - Prob. 44RE Ch. 13 - Prob. 45RE Ch. 13 - Prob. 46RE Ch. 13 - Prob. 47RE Ch. 13 - Prob. 48RE Ch. 13 - Prob. 49RE Ch. 13 - Prob. 50RE Ch. 13 - Prob. 51RE Ch. 13 - Prob. 52RE Ch. 13 - Prob. 53RE Ch. 13 - Prob. 54RE Ch. 13 - Prob. 55RE Ch. 13 - Prob. 56RE Ch. 13 - Prob. 57RE Ch. 13 - Prob. 58RE Ch. 13 - Prob. 59RE Ch. 13 - Prob. 60RE Ch. 13 - Prob. 61RE Ch. 13 - Prob. 62RE Ch. 13 - Prob. 3CS

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