Need Help with Integrating (e^(-x)sin(x))? Find the Solution Here!"

[sara_87]

Homework Statement

what is the integral of (e^(-x)sin(x)) with limits 2 and 1

Homework Equations

The Attempt at a Solution

let the integral be denoted as I
i used integration by parts twice and i got that:
I=[-e^(-x)(sin(x))] + [e^(-x)(sin(x))] + I

i'm stuck now and don't know what to do, can someone help me please.
thank you very much

 

[Dick]

That's perfectly valid, but not very interesting. I think you used the wrong 'part' for one of your integrations by parts. In udv=d(uv)-vdu, you can use either the trig function or the exponential for v. In one integration you used the exponential and in the other the trig. Use the same one for both.

 

[rocomath]

Skim through this post https://www.physicsforums.com/showthread.php?t=209677

It's basically your problem except the angle is different.

 

[arildno]

First off, we get:
$$I=-e^{-x}\sin(x)|^{x=2}_{x=1}+\int{e}^{-x}\cos(x)dx$$
Continue to use e^{-x} as u' in the integration by parts formula.

 

[sara_87]

thanx 2 all
;) ;) ;)