Calculate, using direct integration, the value of e^2t
given that s > -2.
and...
e^t = 1/s-1
for s > 1
Any help on how to do this direct integration would be great guys, thank you
By definition: $\displaystyle LT[f(t)] = \int_0^{+\infty} e^{-st} f(t) \, dt$.
Therefore: $\displaystyle LT\left[ e^{2t} \right] = \int_0^{+\infty} e^{-st} e^{2t} \, dt = \int_0^{+\infty} e^{-t(s-2)} \, dt $.
It's expected you can calculate an improper integral like this one.