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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.7 - Problem 76e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.7 - Problem 76e

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# Laplace transforms A powerful tool in solving problems in ISBN: 9780321570567 2

## Solution for problem 76E Chapter 7.7

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

Step 3 of 3

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