Find the Laplace transform of 1

Answer 1

The Laplace Transform of f(t) is ∫_{(from 0 to ∞)} e^-stf(t)dt.

So, the Laplace Transform of f(t) = 1 is:

∫_{(from 0 to ∞)} e^-stdt = lim_(b→∞) ∫_{(from 0 to b)} e^-stdt = lim_(b→∞) [(-1/s)e^-st_{(from 0 to b)} ]

= (-1/s)lim_(b→∞) [e^-bs - 1] = (-1/s) lim_(b→∞) [1 / e^bs - 1] = (-1/s) [ 0 - 1 ] = 1/s