Solution: Laplace transforms A powerful tool in solving

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

Problem 78E 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 78E

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:

Problem 78E

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 of , the following improper integral is evaluated using integration by parts:

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

Step 1</p>

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</p>

Here we have

Thus … (1)

We shall integrate this by using integration by parts technique.

        Integration by parts is a technique for performing indefinite integration , by expanding the differential of a product of functions  and expressing the original integral in terms of a known integral . Thus we get

  … (2)

Step 3 of 4

Chapter 7.7, Problem 78E is Solved
Step 4 of 4

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

This full solution covers the following key subjects: Laplace, transform, real, Where, transforms. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The full step-by-step solution to problem: 78E from chapter: 7.7 was answered by Sieva Kozinsky, our top Calculus solution expert on 03/03/17, 03:45PM. Calculus: Early Transcendentals was written by Sieva Kozinsky and is associated to the ISBN: 9780321570567. Since the solution to 78E from 7.7 chapter was answered, more than 247 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 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.” is broken down into a number of easy to follow steps, and 71 words. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1.

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