Laplace Transforms small question Watch

LeeC
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From Stroud's Further Engineering Maths..

Where L(F(t)) is the Laplace Transform of a function:

\displaystyle\int^{\infty}_0 {e^{-st}} \, dt = {L(F(t))}

In determining the transform of any function, you will appreciate that the limits are subsituted for t so that the result will be a function of s:

\displaystyle\int^{\infty}_0 {e^{-st}} \, dt = {L(F(t))}={f(s)}

I don't understand the jump from the first equation to the second, how does the Laplace Transform = f(s)?

Thanks
Lee
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barry_4_england
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I think all that it's saying is that as the integral is with respect to t, you are then substituting in t, and so the final result is only a function of s.
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LeeC
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Ok thanks
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