(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm trying to solve a definite Laplace transform. The function is defined as [tex]f(t) = sin(t)[/tex] over the interval [tex][0, \pi][/tex]

2. Relevant equations

The integrate to evaluate is:

[tex]\int_0^\pi e^{-st} sin(t) dt[/tex]

3. The attempt at a solution

To evaluate, first use integration by parts (IBP).

[tex]

\begin{matrix}

u = sin(t) \quad dV = e^{-st} dt\\

du = cos(t) dt \quad V = \frac{e^{-st}}{-s}

\end{matrix}[/tex]

[tex]\int_0^\pi e^{-st} sin(t) dt = \frac{sin(t) e^{-st}}{-s} + \frac{1}{s} \int_0^\pi e^{-st} cos(t) dt[/tex]

However, I'm stuck here. I can try to keep evaluating by parts, but it looks to me like I'm stuck in a loop. Integrating by parts will alternate me between sine and cosine, and the only thing that will change will be the increasing power for the "s" in the denominator.

Any help is greatly appreciated.

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# Homework Help: Laplace transform, need help with integral

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