Question

Using the definition, find the Laplace transform
\[\int\limits_{0}^{\pi}e^{-st}\sin(t)\space dt\]

Answer 1

I'm having trouble with parts on this @zepdrix

Answer 2

Ughhh this is one of those annoying ones D: where you have to do it by parts TWICE, then you'll notice that we ended up with the same thing you started with, and are able to do some algebra from there.

Answer 3

There are a couple ways to do this one using the complex exponential from Euler's Formula... makes it sooooo much easier :D But if you wanna do it the tough way, we can do that XD lol

Answer 4

I don't remember euler. lets do that way. I'm going to google it quick so you don't have to teach it.

Answer 5

Hmm what happened there, your DV doesn't look right, I don't see a (-1/s) attached to that integral.

Answer 6

your right i forgot to type that in

Answer 7

I don't think I was ever taught this Euler way. Where does that come into play. Are you assuming s is complex

Answer 8

\[-\frac{ e^{-st} }{ s }\sin(t)+\frac{ 1 }{ s }\int\limits_{0}^{\pi}e^{-st}\cos(t)\space dt\]

Answer 9

I'll just show you this way real quick, if it's too confusing we can do by parts ^^