Let f(t) be a function on. The Laplace transform of fis the function F defined by the integral . Use this definition to determine the Laplace transform of the following

Elleanor Mckenzie

Elleanor Mckenzie

Answered question

2020-12-27

Let f(t) be a function on [0,). The Laplace transform of fis the function F defined by the integral F(s)=0estf(t)dt . Use this definition to determine the Laplace transform of the following function.
f(t)={1t0<t<101<t

Answer & Explanation

grbavit

grbavit

Skilled2020-12-28Added 109 answers

Step 1
We know that , F(s)=0estf(t)dt
Here f(t)={1t0<t<101<t
from F(s)=0(f(t))estdt=01(1t)estdt+10estdt
=01(1t)estdt+0
F(s)=[(1t)ests(1)ests2]01
F(s)=1s+ess1s2
Step 2
This is required Laplace Transform.

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