If

f(t)

is defined for

t>=0

, then its Laplace transform

F(s)

, also denoted

Lf(s)

or

L[f(t)]

, is defined by\

F(s)=L[f(t)]=\\\\int_0^(\\\\infty ) e^(-st)f(t)dt,

\ for values of

s

for which the improper integral converges.\ Apply the definition above to find the Laplace transform of the following function. (Enter your answer in terms of

s

.)\

f(t)=6te^(t)\ L[f(t)]=

If f(t) is defined for t0, then its Laplace transform F(s), also denoted L(s) or L[f(t)], is defined by F(s)=L[f(t)]=0estf(t)dt, for values of s for which the improper integral converges. Apply the definition above to find the Laplace transform of the following function. (Enter your answer in terms of s.) f(t)=6tet L[f(t)]=