Explanation Given: The given indefinite integral is ∫ Q ( t ) d t . Where Q ( t ) = B 1 + A e − r t Concept used: Integration of a function can be defined by anti derivative of that function. For any function f ( x ) = a x + C , derivative of the function can be evaluated as f ′ ( x ) = a d d x ( x ) + d d x ( C ) = a ( 1 ) + 0 = a Therefore, antiderivative of a is given by ∫ a d x = a x + C Here, a is any constant and C is integrating constant. On other hand, ∫ a d x = a ∫ d x = a x + C Formula used: Formula to evaluate the integral of the form ∫ f ′ ( x ) d x f ( x ) is shown below. ∫ f ′ ( x ) d x f ( x ) = ln | f ( x ) | + C Calculation: Now, consider the given integral

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Differential Equations

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Chapter 5.5, Problem 60PS

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To find:The integral of the given logistic function.

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Chapter 5.5, Problem 59PS

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Chapter 5 Solutions

Calculus

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The integral of the given logistic function.

Solution Summary: The author explains that the integral of the given logistic function can be defined by anti-derivative of that function.

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Chapter 5 Solutions