integral (e^-ax)sin(bx) from 0 to infinity

1. The problem statement, all variables and given/known data



integral (e^-ax)sin(bx) from 0 to infinity



2. Relevant equations







3. The attempt at a solution



I want to check if my answer is right



I got



\frac { \frac { -1 }{ a } { e }^{ -ax }\quad sinbx\quad -\frac { b }{ { a }^{ 2 } } { e }^{ -ax }\quad cosbx }{ 1+\frac { { b }^{ 2 } }{ { a }^{ 2 } } }



and when I did the limit to infinity I got zero?



I'm not sure if it's correct