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Laplace transforms A powerful tool in solving problems in

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

Solution for problem 76E 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 76E

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.

\(f(t)=1 \quad \ \rightarrow \quad \ F(s)=\frac{1}{s}\)

Step-by-Step Solution:

 Step 1 of 3

                  Given ,  the laplace  transform  is a new  function F(s)  defined by

                                        .

                   Now , we have to prove      f(t) = 1 F(s) =  , where a is a real number.

 

 

Step 2 of 3

Chapter 7.7, Problem 76E is Solved
Step 3 of 3

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

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