# Laplace transform proof

show that L{f(t/b)} = bF(bs), b is not equal to 0

i know that
L{f(t)} = $$\int$$e-stf(t) dt = F(s)
so
L{f(t/b)} = $$\int$$e-stf(t/b) dt

any tips on how to start? thx

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Dick
Homework Helper
Do a u substitution to change the integration variable. Substitute u=t/b.

do i also have to plug in (t/b) into e-st so that it becomes e-s(t/b) ?

Dick
Homework Helper
do i also have to plug in (t/b) into e-st so that it becomes e-s(t/b) ?
You need to write e^(-st) in terms of u.

so..
u = t/b
t = bu
e^(-st)
e^(-sbu)

Dick