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Solved: Laplace transforms A powerful tool in solving

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 77E Chapter 7.7

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 77E

Laplace transforms A powerful tool in solving problems in engineering and physics is the Laplace transform. Given a function f(t), the Laplace transform is a new function F(s) defined by

\(F(s)=\int_{0}^{\infty} e^{-s t} f(t) \ d t\),

where we assume then s is a positive real number. For example, to find the Laplace transform oj f(t)= e?t, the following improper integral is evaluated using integration by parts:

\(F(s)=\int_{0}^{\infty} e^{-s t} e^{-t} \ d t=\int_{0}^{\infty} e^{-(s+1) t} \ d t=\frac{1}{s+1}\)

Verify the following Laplace transforms, where a is a real number.

\(f(t)=e^{a t} \quad \ \rightarrow \quad \ F(s)=\frac{1}{s-a}\)

Step-by-Step Solution:

Problem 77E

Laplace transforms A powerful tool in solving problems in engineering and physics is the Laplace transform. Given a function f(t), the Laplace transform is a new function F(s) defined by  where we assume s is a positive real number. For example, to find the Laplace transform of , the following improper integral is evaluated using integration by parts:

Verify the following Laplace transforms, where a is a real number.

Solution

Step 1

In this problem we have to verify the given laplace transform.

That is we have to prove : where a is a real number.

The laplace transform of a function is defined as follows.

Given a function f(t), the Laplace transform is a new function F(s) defined by  where we assume s is a positive real number.

Step 2 of 3

Chapter 7.7, Problem 77E is Solved
Step 3 of 3

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Since the solution to 77E from 7.7 chapter was answered, more than 311 students have viewed the full step-by-step answer. The answer to “?Laplace transforms A powerful tool in solving problems in engineering and physics is the Laplace transform. Given a function f(t), the Laplace transform is a new function F(s) defined by \(F(s)=\int_{0}^{\infty} e^{-s t} f(t) \ d t\),where we assume then s is a positive real number. For example, to find the Laplace transform oj f(t)= e?t, the following improper integral is evaluated using integration by parts:\(F(s)=\int_{0}^{\infty} e^{-s t} e^{-t} \ d t=\int_{0}^{\infty} e^{-(s+1) t} \ d t=\frac{1}{s+1}\)Verify the following Laplace transforms, where a is a real number.\(f(t)=e^{a t} \quad \ \rightarrow \quad \ F(s)=\frac{1}{s-a}\)” is broken down into a number of easy to follow steps, and 94 words. The full step-by-step solution to problem: 77E from chapter: 7.7 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This full solution covers the following key subjects: Laplace, transform, real, Where, transforms. This expansive textbook survival guide covers 112 chapters, and 7700 solutions.

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Solved: Laplace transforms A powerful tool in solving