If f(t) is continuous for t≥0, the Laplace transform of f is the function F defined by this equation. Find the Laplace transforms of the following functions.

Question

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

F(s)=∫(0 to ∞) f(t)e^-stdt

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:

1. f(t)=1
2. f(t)=e^t
3. f(t)=t

Answer 1