Explanation Given information: A function is given by p ( t ) = 1 r e − t r on the interval [ 0 , ∞ ) . Formula used: The indefinite integral can be calculated as shown below. ∫ e − a t d t = e − a t − a + C Calculation: Let us consider the given function. p ( t ) = 1 r e − t r Now let us evaluate the integral ∫ 0 ∞ p ( t ) d t as follows: ∫ 0 ∞ p ( t ) d t = ∫ 0 ∞ 1 r e − t / r d t = lim A → ∞ ∫ 0 A

4th Edition

ISBN: 9781319379421

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 8.1, Problem 12E

To determine

To show:

That p(t) satisfies the condition ∫0∞p(t)dt=1 for all r>0.

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Chapter 8.1, Problem 11E

Chapter 8.1, Problem 13E

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Chapter 8 Solutions

CALCULUS 4E (HC) W/ ACHIEVE ACCESS

Ch. 8.1 - Prob. 1PQ Ch. 8.1 - Prob. 2PQ Ch. 8.1 - Prob. 3PQ Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E

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That p ( t ) satisfies the condition ∫ 0 ∞ p ( t ) d t = 1 for all r > 0 .

Solution Summary: The author explains that p(t) satisfies the condition for the function.

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To show:

That p(t) satisfies the condition ∫0∞p(t)dt=1 for all r>0.

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Chapter 8 Solutions

That p ( t ) satisfies the condition ∫ 0 ∞ p ( t ) d t = 1 for all r &gt; 0 .

Solution Summary: The author explains that p(t) satisfies the condition for the function.

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To show: That p(t) satisfies the condition ∫0∞p(t)dt=1 for all r>0.

Want to see the full answer?

Chapter 8 Solutions

That p ( t ) satisfies the condition ∫ 0 ∞ p ( t ) d t = 1 for all r > 0 .

To show:

That p(t) satisfies the condition ∫0∞p(t)dt=1 for all r>0.