Question

Definition 7.1.1 laplace transform let f be a function defined for t ≥ 0. then the integral script l{f(t)} = [infinity] e−stf(t) dt 0 is said to be the laplace transform of f, provided that the integral converges. to find script l{f(t)}. script l{f(t)} = incorrect: your answer is incorrect. (s > 0)

Answer 1

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/∞) = ∞

F(s) = -(1/s) [0 - 1] = -(1/s) (-1) = (1/s)

Hope this Helps!!!