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Laplace transforms A powerful tool in solving | Ch 7.7 - 80E

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

Solution for problem 80E 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 80E

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 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:

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

Step-by-Step Solution:

Step 1:

We have to verify the Laplace transform of cos at=

Step 2:

By the definition of Laplace transform “Given a function f(t), the Laplace transform is a new function F(s) defined by

   

Step 3 of 4

Chapter 7.7, Problem 80E is Solved
Step 4 of 4

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

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Laplace transforms A powerful tool in solving | Ch 7.7 - 80E

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