Explanation Given information: The provided indefinite integral is ∫ y 2 y 2 + 1 d y . Formula Used: Integration formula: ∫ f ′ ( x ) f ( x ) d x = ln f ( x ) + c differentiation formula: d ( ln x ) d x = 1 x d ( k ) d x = 0 , k is constant Calculation: Consider the indefinite integral, ∫ y 2 y 2 + 1 d y Apply, integration formula ∫ f ′ ( x ) f ( x ) d x = ln f ( x ) + c in ∫ y 2 y 2 + 1 d y Therefore, ∫ y 2 y 2 + 1 d y = 1 4 ∫ 4 y 2 y 2 + 1 d y = 1 4 ln | 2 y 2 + 1 | + c Integration is the inverse process of differentiation

Calculus: An Applied Approach (MindTap Course List)

10th Edition

ISBN: 9781305860919

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 11.2, Problem 4SWU

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To calculate: The value of the indefinite integral ∫y2y2+1dy.

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Chapter 11.2, Problem 3SWU

Chapter 11.2, Problem 5SWU

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Chapter 11 Solutions

Calculus: An Applied Approach (MindTap Course List)

Ch. 11.1 - Checkpoint 1 Worked-out solution available at...Ch. 11.1 - Prob. 2CP Ch. 11.1 - Prob. 3CP Ch. 11.1 - Prob. 4CP Ch. 11.1 - Prob. 1SWU Ch. 11.1 - Prob. 2SWU Ch. 11.1 - Prob. 3SWU Ch. 11.1 - Prob. 4SWU Ch. 11.1 - Prob. 5SWU Ch. 11.1 - Prob. 6SWU

Ch. 11.1 - Verifying Solutions In Exercises 112, verify the...Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Verifying Solutions In Exercises 1-12, verify the...Ch. 11.1 - Prob. 10E Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - Determining Solutions In Exercises 1316, determine...Ch. 11.1 - Prob. 16E Ch. 11.1 - Determining Solutions In Exercises 1720, determine...Ch. 11.1 - Prob. 18E Ch. 11.1 - Prob. 19E Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Prob. 31E Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.1 - Prob. 35E Ch. 11.1 - Prob. 36E Ch. 11.1 - Prob. 37E Ch. 11.1 - Prob. 38E Ch. 11.1 - Prob. 39E Ch. 11.1 - Investment The rate of growth of an investment is...Ch. 11.1 - Prob. 41E Ch. 11.1 - Prob. 42E Ch. 11.1 - Prob. 43E Ch. 11.1 - Prob. 44E Ch. 11.1 - Prob. 45E Ch. 11.1 - Prob. 46E Ch. 11.2 - Checkpoint 1 Worked-out solution available at...Ch. 11.2 - Prob. 2CP Ch. 11.2 - Prob. 3CP Ch. 11.2 - Prob. 4CP Ch. 11.2 - Prob. 5CP Ch. 11.2 - Prob. 6CP Ch. 11.2 - Prob. 1SWU Ch. 11.2 - Prob. 2SWU Ch. 11.2 - Prob. 3SWU Ch. 11.2 - Prob. 4SWU Ch. 11.2 - Prob. 5SWU Ch. 11.2 - Prob. 6SWU Ch. 11.2 - Prob. 7SWU Ch. 11.2 - Prob. 8SWU Ch. 11.2 - Prob. 9SWU Ch. 11.2 - Prob. 10SWU Ch. 11.2 - Prob. 1E Ch. 11.2 - Prob. 2E Ch. 11.2 - Prob. 3E Ch. 11.2 - Prob. 4E Ch. 11.2 - Prob. 5E Ch. 11.2 - Prob. 6E Ch. 11.2 - Prob. 7E Ch. 11.2 - Prob. 8E Ch. 11.2 - Prob. 9E Ch. 11.2 - Prob. 10E Ch. 11.2 - Prob. 11E Ch. 11.2 - Prob. 12E Ch. 11.2 - Prob. 13E Ch. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Prob. 15E Ch. 11.2 - Prob. 16E Ch. 11.2 - Prob. 17E Ch. 11.2 - Prob. 18E Ch. 11.2 - Prob. 19E Ch. 11.2 - Prob. 20E Ch. 11.2 - Prob. 21E Ch. 11.2 - Prob. 22E Ch. 11.2 - Prob. 23E Ch. 11.2 - Prob. 24E Ch. 11.2 - Prob. 25E Ch. 11.2 - Prob. 26E Ch. 11.2 - Prob. 27E Ch. 11.2 - Prob. 28E Ch. 11.2 - Prob. 29E Ch. 11.2 - Prob. 30E Ch. 11.2 - Prob. 31E Ch. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Prob. 33E Ch. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Prob. 35E Ch. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Prob. 37E Ch. 11.2 - Prob. 38E Ch. 11.2 - Prob. 39E Ch. 11.2 - Prob. 40E Ch. 11.2 - Prob. 41E Ch. 11.2 - Prob. 42E Ch. 11.2 - Prob. 43E Ch. 11.2 - Prob. 44E Ch. 11.2 - Radioactive Decay The rate of decomposition of...Ch. 11.2 - Radioactive Decay The rate of decomposition of...Ch. 11.2 - Solve the differential equation. Weight Gain A...Ch. 11.2 - Prob. 1QY Ch. 11.2 - Prob. 2QY Ch. 11.2 - Prob. 3QY Ch. 11.2 - Prob. 4QY Ch. 11.2 - Prob. 5QY Ch. 11.2 - Prob. 6QY Ch. 11.2 - Prob. 7QY Ch. 11.2 - Prob. 8QY Ch. 11.2 - Prob. 9QY Ch. 11.2 - Prob. 10QY Ch. 11.2 - Prob. 11QY Ch. 11.2 - Prob. 12QY Ch. 11.2 - Prob. 13QY Ch. 11.2 - Prob. 14QY Ch. 11.2 - Prob. 15QY Ch. 11.2 - Ignoring resistance, a sailboat starting from rest...Ch. 11.3 - Checkpoint 1 Worked-out solution available at...Ch. 11.3 - Prob. 2CP Ch. 11.3 - Prob. 3CP Ch. 11.3 - Prob. 1SWU Ch. 11.3 - Prob. 2SWU Ch. 11.3 - Prob. 3SWU Ch. 11.3 - Prob. 4SWU Ch. 11.3 - Prob. 5SWU Ch. 11.3 - Prob. 6SWU Ch. 11.3 - Prob. 7SWU Ch. 11.3 - Prob. 8SWU Ch. 11.3 - In Exercises 5-10, find the indefinite integral....Ch. 11.3 - Prob. 10SWU Ch. 11.3 - Prob. 1E Ch. 11.3 - Prob. 2E Ch. 11.3 - Prob. 3E Ch. 11.3 - Prob. 4E Ch. 11.3 - Prob. 5E Ch. 11.3 - Prob. 6E Ch. 11.3 - Prob. 7E Ch. 11.3 - Prob. 8E Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Prob. 10E Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Prob. 13E Ch. 11.3 - Prob. 14E Ch. 11.3 - Prob. 15E Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Prob. 17E Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Using Two Methods In Exercises 19-22, solve for y...Ch. 11.3 - Prob. 20E Ch. 11.3 - Prob. 21E Ch. 11.3 - Prob. 22E Ch. 11.3 - Prob. 23E Ch. 11.3 - Prob. 24E Ch. 11.3 - Prob. 25E Ch. 11.3 - Prob. 26E Ch. 11.3 - Prob. 27E Ch. 11.3 - Prob. 28E Ch. 11.3 - Prob. 29E Ch. 11.3 - Prob. 30E Ch. 11.3 - Prob. 31E Ch. 11.3 - Prob. 32E Ch. 11.3 - Finding a Particular Solution In Exercises 27-34,...Ch. 11.3 - Prob. 34E Ch. 11.3 - Prob. 35E Ch. 11.3 - Prob. 36E Ch. 11.3 - Vertical Motion A falling object encounters air...Ch. 11.3 - Velocity A booster rocket carrying an observation...Ch. 11.3 - Learning Curve The management at a medical supply...Ch. 11.3 - Investment Let A he the amount in a fund earning...Ch. 11.4 - Prob. 1CP Ch. 11.4 - Prob. 2CP Ch. 11.4 - Checkpoint 3 Worked-out solution available at...Ch. 11.4 - Prob. 4CP Ch. 11.4 - Checkpoint 5 Worked-out solution available at...Ch. 11.4 - Prob. 1SWU Ch. 11.4 - Prob. 2SWU Ch. 11.4 - Prob. 3SWU Ch. 11.4 - Prob. 4SWU Ch. 11.4 - Prob. 5SWU Ch. 11.4 - Prob. 6SWU Ch. 11.4 - Prob. 7SWU Ch. 11.4 - Prob. 8SWU Ch. 11.4 - Prob. 9SWU Ch. 11.4 - Prob. 10SWU Ch. 11.4 - Prob. 1E Ch. 11.4 - Prob. 2E Ch. 11.4 - Advertising Awareness In Exercises 3 and 4, use...Ch. 11.4 - Prob. 4E Ch. 11.4 - Prob. 5E Ch. 11.4 - Prob. 6E Ch. 11.4 - Prob. 7E Ch. 11.4 - Prob. 8E Ch. 11.4 - Prob. 9E Ch. 11.4 - Prob. 10E Ch. 11.4 - Prob. 11E Ch. 11.4 - Prob. 12E Ch. 11.4 - Prob. 13E Ch. 11.4 - Prob. 14E Ch. 11.4 - Prob. 15E Ch. 11.4 - Prob. 16E Ch. 11.4 - Prob. 17E Ch. 11.4 - Chemistry A wet towel hung from a clothesline to...Ch. 11.4 - Prob. 19E Ch. 11.4 - Prob. 20E Ch. 11.4 - Biology A population of eight beavers has been...Ch. 11.4 - Prob. 22E Ch. 11.4 - Prob. 23E Ch. 11.4 - Prob. 24E Ch. 11.4 - 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Prob. 33RE Ch. 11 - Prob. 34RE Ch. 11 - Prob. 35RE Ch. 11 - Prob. 36RE Ch. 11 - Prob. 37RE Ch. 11 - Prob. 38RE Ch. 11 - Prob. 39RE Ch. 11 - Prob. 40RE Ch. 11 - Prob. 41RE Ch. 11 - Solving a Differential Equation In Exercises...Ch. 11 - Prob. 43RE Ch. 11 - Prob. 44RE Ch. 11 - Prob. 45RE Ch. 11 - Prob. 46RE Ch. 11 - Prob. 47RE Ch. 11 - Prob. 48RE Ch. 11 - Prob. 49RE Ch. 11 - Prob. 50RE Ch. 11 - Prob. 51RE Ch. 11 - Prob. 52RE Ch. 11 - Prob. 53RE Ch. 11 - Prob. 54RE Ch. 11 - Prob. 55RE Ch. 11 - Prob. 56RE Ch. 11 - Solving a Linear Differential Equation In...Ch. 11 - Prob. 58RE Ch. 11 - Prob. 59RE Ch. 11 - Prob. 60RE Ch. 11 - Prob. 61RE Ch. 11 - Prob. 62RE Ch. 11 - Prob. 63RE Ch. 11 - Prob. 64RE Ch. 11 - Prob. 65RE Ch. 11 - Prob. 66RE Ch. 11 - Safety Assume the rate of change per hour in the...Ch. 11 - Prob. 68RE Ch. 11 - Prob. 69RE Ch. 11 - Prob. 70RE Ch. 11 - Prob. 71RE Ch. 11 - Prob. 72RE Ch. 11 - Prob. 73RE Ch. 11 - Prob. 74RE Ch. 11 - Prob. 75RE Ch. 11 - Chemical Mixture A tank contains 30 gallons of a...Ch. 11 - Chemical Mixture A tank contains 20 gallons of a...Ch. 11 - Prob. 1TYS Ch. 11 - Prob. 2TYS Ch. 11 - Prob. 3TYS Ch. 11 - Prob. 4TYS Ch. 11 - Prob. 5TYS Ch. 11 - Prob. 6TYS Ch. 11 - Prob. 7TYS Ch. 11 - Prob. 8TYS Ch. 11 - Prob. 9TYS Ch. 11 - Prob. 10TYS Ch. 11 - Prob. 11TYS Ch. 11 - A lamb that weighs 10 pounds at birth gains weight...Ch. 11 - Prob. 13TYS

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The value of the indefinite integral ∫ y 2 y 2 + 1 d y .

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To calculate: The value of the indefinite integral ∫y2y2+1dy.

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Chapter 11 Solutions