Question

Differential Equations: The definite integral [integral sign from 0 --> infinity] te^[(4-s)t]dt represents the Laplace transform of which function?

Answer 1

Equation in a better form: \[\int\limits_{0}^{\infty} te ^{(4-s)t}dt\]

Answer 2

The integrand for the transform is e^(-st)*f(t).
So we need to isolate the e^(-st)
te^(4-s)t=te^(4t)*e^(-st) by the properties of exponents
So we can see f(t) there as te^(4t)

Answer 3

so that's it? whatever is left over after the e^(-st) was isolated is what was transformed?

Answer 4

Yes

Answer 5

awesome, thanks!