Answer:
The Laplace transform of f(t) = 1 is given by
F(s) = (1/s) for all s>0
Step-by-step explanation:
Laplace transform of a function f(t) is given as
F(s) = ∫∞₀ f(t) e⁻ˢᵗ dt
Find the Laplace transform for when f(t) = 1
F(s) = ∫∞₀ 1.e⁻ˢᵗ dt
F(s) = ∫∞₀ e⁻ˢᵗ dt = (1/s) [-e⁻ˢᵗ]∞₀
= -(1/s) [1/eˢᵗ]∞₀
Note that e^(∞) = ∞
F(s) = -(1/s) [(1/∞) - (1/e⁰)]
Note that (1/∞) = 0
F(s) = -(1/s) [0 - 1] = -(1/s) (-1) = (1/s)
Hope this Helps!!!
In this exercise we have to use the knowledge of the Laplace transform to calculate the total value of the given function, thus we will find that:
[tex]F(s) = (1/s) \\for \ all\ s>0[/tex]
So we have that the Laplace transform can be recognized as:
[tex]F(s) = \int\limits^\infty _0 { f(t) e^{-st} \, dt[/tex]
Find the Laplace transform for when f(t) = 1, we have that:
[tex]F(s) = \int\limits^\infty _0 { f(t) e^{-st} \, dt \\\\ F(s) = \int\limits^\infty _0 { 1 e^{-st} \, dt[/tex]
[tex]F(s) = \int\limits^\infty _0 { e^{-st} \, dt = (1/s) [-e^{-st}] \\[/tex]
[tex]F(s) = -(1/s) [(1/\infty ) - (1/e^0)] \\F(s) = -(1/s) [0 - 1] = -(1/s) (-1) = (1/s)[/tex]
See more about Laplace transform at brainly.com/question/2088771
