Question

Find the Laplace transform using the definition: y{f(t)} = ∫[0 to [infinity]] e^(-st) * f(t) dt

(1) f(t) = 1-t
(4) f(t) =

Answer 1

To find the Laplace transform using the given definition, substitute the function into the integral and simplify.

Step-by-step explanation:

The Laplace transform of a function f(t) using the definition is given by the integral:

y{f(t)} = ∫[0 to ∞] e^(-st) * f(t) dt

To find the Laplace transform of f(t) = 1 - t, we substitute this function into the integral:

y{f(t)} = ∫[0 to ∞] e^(-st) * (1 - t) dt

Next, we simplify and integrate the expression to find the Laplace transform.