Explanation Given Information: The provided improper integral is ∫ 0 ∞ 3 e − 3 t ⋅ d t . Formula used: If the limit defining the improper integral is a unique finite number, then integral converges else it diverges, ∫ a ∞ f ( x ) d x = lim b → ∞ ∫ a b f ( x ) d x According to the exponential rule of integrals, ∫ e x d x = e x + C Calculation: Consider the given equation, I = ∫ 0 ∞ 3 e − 3 t Now, use the formula, ∫ a ∞ f ( x ) d x = lim b → ∞ ∫ a b f ( x ) d x to rewrite the integral as, I = ∫ 0 ∞ 3 e − 3 t = lim b → ∞ ∫ 0 b 3 e − 3 t d x Now, integrate, I = lim b → ∞ ∫ 0 b 3 e ȡ

Calculus: An Applied Approach (MindTap Course List)

10th Edition

ISBN: 9781305860919

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 9.2, Problem 7SWU

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To calculate: The solution of the improper integral ∫0∞3e−3t⋅dt

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Chapter 9.2, Problem 6SWU

Chapter 9.2, Problem 1E

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Chapter 9 Solutions

Calculus: An Applied Approach (MindTap Course List)

Ch. 9.1 - Checkpoint 1 Worked-out solution available at...Ch. 9.1 - Prob. 2CP Ch. 9.1 - Prob. 3CP Ch. 9.1 - Prob. 4CP Ch. 9.1 - Prob. 5CP Ch. 9.1 - Prob. 6CP Ch. 9.1 - Prob. 1SWU Ch. 9.1 - Prob. 2SWU Ch. 9.1 - Prob. 3SWU Ch. 9.1 - Prob. 4SWU

Ch. 9.1 - Prob. 5SWU Ch. 9.1 - Prob. 6SWU Ch. 9.1 - Prob. 7SWU Ch. 9.1 - Prob. 8SWU Ch. 9.1 - Prob. 9SWU Ch. 9.1 - Prob. 10SWU Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Random Selection A card is chosen at random from a...Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E Ch. 9.1 - Identifying Probability Distributions In Exercises...Ch. 9.1 - Prob. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - Prob. 14E Ch. 9.1 - Prob. 15E Ch. 9.1 - Using Probability Distributions In Exercises 1518,...Ch. 9.1 - Prob. 17E Ch. 9.1 - Prob. 18E Ch. 9.1 - Prob. 19E Ch. 9.1 - Children The table shows the probability...Ch. 9.1 - Prob. 21E Ch. 9.1 - Die Roll Consider the experiment of rolling a...Ch. 9.1 - Prob. 23E Ch. 9.1 - Prob. 24E Ch. 9.1 - Prob. 25E Ch. 9.1 - Prob. 26E Ch. 9.1 - Prob. 27E Ch. 9.1 - Prob. 28E Ch. 9.1 - Prob. 29E Ch. 9.1 - Personal Income The probability distribution of...Ch. 9.1 - Insurance An insurance company needs to determine...Ch. 9.1 - 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The solution of the improper integral ∫ 0 ∞ 3 e − 3 t ⋅ d t

Solution Summary: The author explains that the solution of the improper integral is 1. If the limit defining it is a unique finite number, then it diverges.

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To calculate: The solution of the improper integral ∫0∞3e−3t⋅dt

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Chapter 9 Solutions