2. Use integration by parts to prove the following reduction formula for integrals, where n is a positive integer: 3. Use the result of question 2 to prove that L{t"} = "c{r-1}.
2. Use integration by parts to prove the following reduction formula for integrals, where n is a positive integer: 3. Use the result of question 2 to prove that L{t"} = "c{r-1}.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Question 2:**
Use integration by parts to prove the following reduction formula for integrals, where \( n \) is a positive integer:
\[
\int t^n e^{-st} dt = -\frac{1}{s} t^n e^{-st} + \frac{n}{s} \int t^{n-1} e^{-st} dt
\]
**Question 3:**
Use the result of question 2 to prove that
\[
\mathcal{L}\{t^n\} = \frac{n}{s} \mathcal{L}\{t^{n-1}\}.
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7d7f8ba3-ac35-40be-9d69-f75baa192b25%2F1a599abe-d91b-4c34-a4ab-7aba91181f6e%2Fzthbien_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 2:**
Use integration by parts to prove the following reduction formula for integrals, where \( n \) is a positive integer:
\[
\int t^n e^{-st} dt = -\frac{1}{s} t^n e^{-st} + \frac{n}{s} \int t^{n-1} e^{-st} dt
\]
**Question 3:**
Use the result of question 2 to prove that
\[
\mathcal{L}\{t^n\} = \frac{n}{s} \mathcal{L}\{t^{n-1}\}.
\]
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