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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![**Use Definition 7.1.1.**
**DEFINITION 7.1.1 Laplace Transform**
Let \( f \) be a function defined for \( t \geq 0 \). Then the integral
\[
\mathcal{L}\{f(t)\} = \int_{0}^{\infty} e^{-st}f(t) \, dt
\]
is said to be the **Laplace transform** of \( f \), provided that the integral converges.
Find \( \mathcal{L}\{f(t)\} \). (Write your answer as a function of \( s \).)
\( f(t) = e^{-t} \sin t \)
\[
\mathcal{L}\{f(t)\} = \boxed{\phantom{answer}} \quad (s > -1)
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff9cdbf72-d206-4fdd-bded-1942fceb9e15%2Ffc085682-9966-4f6b-8e16-b639587ca070%2Fz5az1yq_processed.png&w=3840&q=75)
Transcribed Image Text:**Use Definition 7.1.1.**
**DEFINITION 7.1.1 Laplace Transform**
Let \( f \) be a function defined for \( t \geq 0 \). Then the integral
\[
\mathcal{L}\{f(t)\} = \int_{0}^{\infty} e^{-st}f(t) \, dt
\]
is said to be the **Laplace transform** of \( f \), provided that the integral converges.
Find \( \mathcal{L}\{f(t)\} \). (Write your answer as a function of \( s \).)
\( f(t) = e^{-t} \sin t \)
\[
\mathcal{L}\{f(t)\} = \boxed{\phantom{answer}} \quad (s > -1)
\]
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