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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.7 - Problem 77e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.7 - Problem 77e

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# Solved: Laplace transforms A powerful tool in solving

ISBN: 9780321570567 2

## Solution for problem 77E Chapter 7.7

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

Step 3 of 3

##### 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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