Explanation Definition used: If f ( t ) is a piecewise continuous function and exponential of order t > 0 such that f ( t ) is defined in two pieces; then Laplace transform of f ( t ) is expressed as the sum of two integrals. L { f ( t ) } = ∫ 0 ∞ e − s t f ( t ) d t = ∫ 0 a e − s t f ( t ) d t + ∫ a ∞ e − s t f ( t ) d t Calculation: Observe that the function in the given graph is f ( t ) = { 0 , 0 ≤ t < 1 t , t ≥ 1 . Note that, the domain of f ( t ) is splits into two parts, 0 to 1 and 1 to ∞ . Use the above definition to write the Laplace transform of the given function. L { f ( t ) } = ∫ 0 1 e − s t ( 0 ) d t + ∫ 1 ∞ e − s t ( t ) d t = [ 0 ] 0 1 + [ t [ e − s t − s ] − ∫ ( 1 ) [ e − s t − s ] d t ] 1 ∞ d t ( ∵ ∫ ( f ⋅ g

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Differential Equations

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Chapter 4.1, Problem 7E

To determine

To find: The expression for the Laplace transform of the given function

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Chapter 4.1, Problem 6E

Chapter 4.1, Problem 8E

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Chapter 4 Solutions

Advanced Engineering Mathematics

Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

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