the question is
find the fourier transform of
g(t) = exp(-t)sin(2*pi*fc*t)u(t) where u(t) is the unit step function
I have the solution which is 2*pi*fc/ (1+4*pi^2 (f-fc)^2)
however, I'm getting stuck at a certain point.
I get as far as....
(1/2j)*( exp[j*2pi(fc-f)t-t] - exp[-j*2pi(fc+f)t-t] )
However when they integrate, they somehow make the fc+f into a fc-f, which I dont understand how they do it.
See attached file for question and solution. I dont understand the 4 line. Any thoughts ?
Thanks !