Homework Help: Integral (e^-ax)sin(bx) from 0 to infinity

1. Jan 1, 2014

applestrudle

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

2. Jan 1, 2014

vela

Staff Emeritus
Yup, that's right. The result of the integral is what you get from the lower limit x=0.

3. Jan 1, 2014

thanks