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

[applestrudle]

Homework Statement

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

Homework Equations

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

 

[vela]

Homework Statement

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

Homework Equations

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

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

 

[applestrudle]

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

thanks