Question

Use the definition of Laplace transform to find the transform of f(t)= sinh t.
Recall: sinh t=1/2(e^t-e^(-t))

Answer 1

yes then go for it

Answer 2

\[L(\sinh~at)=\int\limits_{0}^{\infty}e^{-st}.\frac{ e^{at}-e^{-at} }{ 2 }dt\]

Answer 3

can u do it now?

Answer 4

\[L(\sinh~ t)=\int\limits_{0}^{\infty}e^{-st}\frac{ e^t-e^{-t} }{ 2 }\\=\frac{ 1 }{ 2 }[\int\limits_{0}^{\infty}e^{-st}.e^t-\int\limits_{0}^{\infty}e^{-st}.e^{-t}]\\=\frac{ 1 }{ 2 }[L(e^{t})-L(e^{-t})]=\frac{ 1 }{ 2 }[\frac{ 1 }{ s-1 }-\frac{ 1 }{ s+1 }]\]
i believe u can do the rest :)
@keynote

Answer 5

So where do i from here