Trying to figure out if this book is wrong.
If anybody knows how to do these, would you mind preforming a Laplace transform on the following function:

f(t) = sin(t) on 0<t<pi
f(t) = 0 on pi < t

Seems simple enough but I'm not getting (e^(-pi x s)) / (s^2 + 1) for all s.
which is what the book is getting.

will throw my fg at a satisfactory answer of how to get what the book was, or if your answer agrees with what I got and you show your work.


This post was edited by ringo794 on Apr 12 2015 06:37pm

Answer should be
e^(-π * s) + 1 / (s² + 1)

L(f)(s) = F(s) = ∫(0 to pi) sint * e^(-st) dt
recall sint = (1/2)i (e^(-it) - e^(it)) where i is the imaginary unit

∫(0 to pi) (1/2)i (e^(-it) - e^(it)) * e^(-st) dt

(1/2)i∫(0 to pi) (e^(-(i+s)t) - e^((i-s)t)) dt

(1/2)i [(e^(-(i+s)t) / (-(i+s)) - e^((i-s)t))/(i-s) from 0 to pi

after getting a common denominator and simplify a bit, you get

= e^(-pi * s) / (s² + 1) - (-1/(s² + 1))

= e^(-pi * s) + 1 / (s² + 1)

Thanks for the help, I tried to generally solve for L(sin(bt)) and kind of ignored the boundary conditions
was where my problem came from.