If f(t) is continuous for t ≥0 , the Laplace transform of f is the function F defined by F(s) =

Name: Problem 73, Chapter 7: Calculus: Early Transcendentals
Uploaded: 2018-03-22T20:06:15-08:00
Duration: 3 min 40 s
Channel: Wen Zheng
Description: If f(t) is continuous for t ≥0 , the Laplace transform of f is the function F defined by F(s) = ∫0^∞f(t) e^-st dt and the domain of F is the set consisting of all numbers s for which the integral converges. Find the Laplace transforms of the following functions. (a) f(t) = 1 (b) f(t) = e^t (c) f(t) = t

step 1 If ft is continuous for t is greater than zero, the Laplace transform of f is a function, capita

Question

If $ f(t) $ is continuous for $ t \ge 0 $, the Laplace transform of $ f $ is the function $ F $ defined by $$ F(s) = \int_0^\infty f(t) e^{-st}\ dt $$ and the domain of $ F $ is the set consisting of all numbers s for which the integral converges. Find the Laplace transforms of the following functions. (a) $ f(t) = 1 $ (b) $ f(t) = e^t $ (c) $ f(t) = t $

   If $ f(t) $ is continuous for $ t \ge 0 $, the Laplace transform of $ f $ is the function $ F $ defined by
$$ F(s) = \int_0^\infty f(t) e^{-st}\ dt $$
and the domain of $ F $ is the set consisting of all numbers s for which the integral converges. Find the Laplace transforms of the following functions.
(a) $ f(t) = 1 $                       (b) $ f(t) = e^t $              (c) $ f(t) = t $

Calculus: Early Transcendentals

James Stewart 8th Edition

Chapter 7, Problem 73

Instant Answer

Solved by Expert Wen Zheng

03/22/2018

Step 1

The Laplace transform of $f$ is given by $$ F(s) = \int_0^\infty f(t) e^{-st}\ dt = \int_0^\infty e^{-st}\ dt. $$ We can solve this integral by using the formula for the integral of an exponential function, which gives us $$ F(s) = \lim_{a \to \infty} \left[ Show more…

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If $ f(t) $ is continuous for $ t \ge 0 $, the Laplace transform of $ f $ is the function $ F $ defined by $$ F(s) = \int_0^\infty f(t) e^{-st}\ dt $$ and the domain of $ F $ is the set consisting of all numbers s for which the integral converges. Find the Laplace transforms of the following functions. (a) $ f(t) = 1 $ (b) $ f(t) = e^t $ (c) $ f(t) = t $