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Prove: If L[F(t)] = f(s), then


             ole.gif


Proof. Let


             ole1.gif


Then

 

1)        G'(t) = F(t)


and G(0) = 0. Taking the Laplace transform of both sides gives

 

2)        L[G'(t)] = L[F(t)] = f(s)


Also, from the formula for the transform of a derivative we have

 

3)        L[G'(t)] = sL[G(t)] - G(0) = sL[G(t)]


From 2) and 3) we get


4)        sL[G(t)] = f(s)


Thus


             ole2.gif


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Website owner:  James Miller


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