Question

HELP ME SOLVE THE LAPLACE TRANSFORM OF FOLLOWING FUNCTION
f(t)={sint; 0r

Answer 1

The easy waty to do this is to write the sin as Im (e^{it}), then

\[\int\limits_{0}^{r} e^{-st} e^{\it} dt ={{e^{-sr} e^{ir} -1}\over {-s+i}}\]

then take the Im part to get the answer.