Explanation The Laplace transform of a function can be written as L { f ( t ) } = ∫ 0 ∞ e − s t f ( t ) d t where t > 0 . Thus, the Laplace transform of the t α is, L { t α } = ∫ 0 ∞ e − s t t α d t . Substitute u = s t and d u = s d t in the expression L { t α } = ∫ 0 ∞ e − s t t α d t , L { t α } = ∫ 0 ∞ t α e − s t d t = ∫ 0 ∞ ( u s ) α<

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ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 4.1, Problem 42E

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To show that: The equation L{tα}=Γ(α+1)sα+1 where α>−1.

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Chapter 4.1, Problem 41E

Chapter 4.1, Problem 43E

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Chapter 4 Solutions

Advanced Engineering Mathematics

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To show that: The equation L { t α } = Γ ( α + 1 ) s α + 1 where α > − 1 .

Solution Summary: The author explains the Laplace transform of a function as Llefttalpha right=displaystyle

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To show that: The equation L{tα}=Γ(α+1)sα+1 where α>−1.

Want to see the full answer?

Chapter 4 Solutions

To show that: The equation L { t α } = Γ ( α + 1 ) s α + 1 where α &gt; − 1 .

Solution Summary: The author explains the Laplace transform of a function as Llefttalpha right=displaystyle

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To show that: The equation L{tα}=Γ(α+1)sα+1 where α>−1.

Want to see the full answer?

Chapter 4 Solutions

To show that: The equation L { t α } = Γ ( α + 1 ) s α + 1 where α > − 1 .