Hi i'm lookin for the integral of t*exp(-abs(t))sin(wt) dt with limits at +infinity and -infinity
Anyone available to help?
Write it as two separate integrals:
Apply integration by parts:
Therefore, and (you get v by using integration by parts...again...
Plugging into the integration by parts formula:
Before we move on, note that converges to 0.
Thus, we have left:
Apply integration by parts (again) for these two integals:
I will leave steps out, hoping that you can do it on your own.
Now, the integrals should become
Since we only evaluated half of the integral, double it to get the answer:
Hope that this made sense!!