Laplace Transform equation help

[jesuslovesu]

[SOLVED] Laplace Transform

Homework Statement

Suppose F(s) = \displaystyle\mathcal{L}(f(t))
Show that \displaystyle\mathcal{L}(f(ct)) = 1/c F(s/c)

Homework Equations

The Attempt at a Solution

\displaystyle\mathcal{L}(f(t)) = \int_0^{inf} e^{-st} f(t) dt
\displaystyle\mathcal{L}(f(ct)) = \int_0^{inf} e^{-st} f(ct) dt
I'm not quite sure what to do after this...

I could play around with integration by parts, but in this case I don't think it yields anything useful
\frac{F(ct)}{c} e^{-st} - \int \frac{F(ct)}{c} (-s e^{-st} ) dt

{F(t)e^{-st} + \int F(t) se^{-st} dt}{}

 

[dirk_mec1]

Suppose u=ct then we get:

\int_0^{ \infty} e^{-st} f(ct)\ \mbox{d}t = \frac{1}{c} \int_0^{\infty}\ e^{\frac{-s}{c} u}\ f(u)\ \mbox{d}u = \frac{1}{c}\ F \left( \frac{s}{c} \right)