Explanation Given Information: The equation of the graph that provides shaded region is y = 4 x e − 2 x 2 and the graph is, Formula used: From definition of improper integral . If on the interval [ a , ∞ ) , the function is continuous, then ∫ a ∞ f ( x ) d x = lim b → ∞ ∫ a b f ( x ) d x The integral formula: ∫ e a x = e a x a + C Calculation: Consider the provided equation: ∫ 0 ∞ 4 x e − 2 x 2 d x And the graph is, Use the definition of improper integral ∫ a ∞ f ( x ) d x = lim b → ∞ ∫ a b f ( x ) d x And simplify as ∫ 0 ∞ 4 x e − 2 x 2 d x = lim b → ∞ ∫ 0 b 4 x e − 2 x 2 d x In the provided integral, Assume 2 x 2 = u Now, differentiate 4 x d x = d u Now, substitute the

Calculus: An Applied Approach (MindTap Course List)

10th Edition

ISBN: 9781305860919

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 6, Problem 60RE

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To calculate: The area under the shaded region by the graph of the equation y=4xe−2x2

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Chapter 6, Problem 59RE

Chapter 6, Problem 61RE

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Part 3 of 4 The area of the shaded region is -0.12 X 1.72

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Calculus: An Applied Approach (MindTap Course List)

Ch. 6.1 - Prob. 1CP Ch. 6.1 - Prob. 2CP Ch. 6.1 - Prob. 3CP Ch. 6.1 - Prob. 4CP Ch. 6.1 - Prob. 5CP Ch. 6.1 - Prob. 6CP Ch. 6.1 - Prob. 7CP Ch. 6.1 - Prob. 1SWU Ch. 6.1 - Prob. 2SWU Ch. 6.1 - Prob. 3SWU

Ch. 6.1 - Prob. 4SWU Ch. 6.1 - Prob. 5SWU Ch. 6.1 - Prob. 6SWU Ch. 6.1 - Prob. 7SWU Ch. 6.1 - Prob. 8SWU Ch. 6.1 - Prob. 9SWU Ch. 6.1 - Prob. 10SWU Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Integration by Parts In Exercises 5-16, use...Ch. 6.1 - Prob. 6E Ch. 6.1 - Integration by Parts In Exercises 5-16, use...Ch. 6.1 - Prob. 8E Ch. 6.1 - Integration by Parts In Exercises 5-16, use...Ch. 6.1 - Prob. 10E Ch. 6.1 - Integration by Parts In Exercises 5-16, use...Ch. 6.1 - Prob. 12E Ch. 6.1 - Integration by Parts In Exercises 5-16, use...Ch. 6.1 - Prob. 14E Ch. 6.1 - Integration by Parts In Exercises 5-16, use...Ch. 6.1 - Prob. 16E Ch. 6.1 - Prob. 17E Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Finding an Indefinite Integral In Exercises 17-38,...Ch. 6.1 - Finding an Indefinite Integral In Exercises 17-38,...Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Finding an Indefinite Integral In Exercises 17-38,...Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Prob. 32E Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Finding an Indefinite Integral In Exercises 17-38,...Ch. 6.1 - Finding an Indefinite Integral In Exercises 17-38,...Ch. 6.1 - Prob. 39E Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Evaluating a Definite Integral In Exercises 39-46,...Ch. 6.1 - Prob. 43E Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Prob. 48E Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.1 - Prob. 51E Ch. 6.1 - Prob. 52E Ch. 6.1 - Verifying Formulas In Exercises 53 and 54, use...Ch. 6.1 - Verifying Formulas In Exercises 53 and 54, use...Ch. 6.1 - Prob. 55E Ch. 6.1 - Prob. 56E Ch. 6.1 - Prob. 57E Ch. 6.1 - Prob. 58E Ch. 6.1 - Prob. 59E Ch. 6.1 - Prob. 60E Ch. 6.1 - Prob. 61E Ch. 6.1 - Prob. 62E Ch. 6.1 - Prob. 63E Ch. 6.1 - Prob. 64E Ch. 6.1 - Prob. 65E Ch. 6.1 - Revenue A company sells a seasonal product. 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Prob. 9E Ch. 6.3 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6.3 - Prob. 11E Ch. 6.3 - Prob. 12E Ch. 6.3 - Prob. 13E Ch. 6.3 - Prob. 14E Ch. 6.3 - Prob. 15E Ch. 6.3 - Prob. 16E Ch. 6.3 - Prob. 17E Ch. 6.3 - Prob. 18E Ch. 6.3 - Prob. 19E Ch. 6.3 - Prob. 20E Ch. 6.3 - Prob. 31E Ch. 6.3 - Prob. 32E Ch. 6.3 - Prob. 33E Ch. 6.3 - Prob. 34E Ch. 6.3 - Prob. 35E Ch. 6.3 - Prob. 36E Ch. 6.3 - Prob. 37E Ch. 6.3 - Prob. 38E Ch. 6.3 - Prob. 39E Ch. 6.3 - Error Analysis In Exercises 37-40, use the error...Ch. 6.3 - Prob. 43E Ch. 6.3 - Electricity The table shows the residential prices...Ch. 6.3 - Prob. 45E Ch. 6.3 - Prob. 46E Ch. 6.3 - Prob. 47E Ch. 6.3 - Prob. 48E Ch. 6.4 - Prob. 1CP Ch. 6.4 - Prob. 2CP Ch. 6.4 - Prob. 3CP Ch. 6.4 - Prob. 4CP Ch. 6.4 - Prob. 5CP Ch. 6.4 - Prob. 1SWU Ch. 6.4 - Prob. 2SWU Ch. 6.4 - Prob. 3SWU Ch. 6.4 - Prob. 4SWU Ch. 6.4 - Prob. 5SWU Ch. 6.4 - Prob. 6SWU Ch. 6.4 - Prob. 7SWU Ch. 6.4 - Prob. 8SWU Ch. 6.4 - Prob. 9SWU Ch. 6.4 - Prob. 10SWU Ch. 6.4 - Prob. 1E Ch. 6.4 - 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Prob. 8RE Ch. 6 - Prob. 9RE Ch. 6 - Prob. 10RE Ch. 6 - Prob. 11RE Ch. 6 - Prob. 12RE Ch. 6 - Prob. 13RE Ch. 6 - Prob. 14RE Ch. 6 - Finding Present Value In Exercises 1316, find the...Ch. 6 - Prob. 16RE Ch. 6 - Prob. 17RE Ch. 6 - Prob. 18RE Ch. 6 - Prob. 19RE Ch. 6 - Prob. 20RE Ch. 6 - Prob. 21RE Ch. 6 - Prob. 22RE Ch. 6 - Prob. 23RE Ch. 6 - Prob. 24RE Ch. 6 - Prob. 25RE Ch. 6 - Prob. 26RE Ch. 6 - Prob. 27RE Ch. 6 - Prob. 28RE Ch. 6 - Prob. 29RE Ch. 6 - Prob. 30RE Ch. 6 - Prob. 31RE Ch. 6 - Prob. 32RE Ch. 6 - Prob. 33RE Ch. 6 - Prob. 34RE Ch. 6 - Prob. 35RE Ch. 6 - Prob. 36RE Ch. 6 - Prob. 37RE Ch. 6 - Prob. 38RE Ch. 6 - Prob. 39RE Ch. 6 - Prob. 40RE Ch. 6 - Prob. 41RE Ch. 6 - Prob. 42RE Ch. 6 - Prob. 43RE Ch. 6 - Prob. 44RE Ch. 6 - Prob. 45RE Ch. 6 - Prob. 46RE Ch. 6 - Prob. 47RE Ch. 6 - Prob. 48RE Ch. 6 - Prob. 49RE Ch. 6 - Prob. 50RE Ch. 6 - Prob. 51RE Ch. 6 - Prob. 52RE Ch. 6 - Prob. 53RE Ch. 6 - Prob. 54RE Ch. 6 - Prob. 55RE Ch. 6 - Prob. 56RE Ch. 6 - Prob. 57RE Ch. 6 - Prob. 58RE Ch. 6 - 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The area under the shaded region by the graph of the equation y = 4 x e − 2 x 2

Solution Summary: The author explains how to calculate the area under the shaded region by the graph of the equation.

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To calculate: The area under the shaded region by the graph of the equation y=4xe−2x2

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Chapter 6 Solutions