The question is read
integrate---
int(0 to infinity) (e^-x)(sinx)
So i first expressed this as a limit where
limit A approaching infinity (int 0 to A)(e^-x)(sinx).
I integrated by parts twice to find that int of (e^-x)(sinx) = (e^-x (-sinx-cosx))/2
But now i am stuck on solving the limit itself. Any help is appreciated Thanks in advance
sorry the actual question read int (from 0 to infinity) 2(e^-x)sin(x) which was integrated by parts again twice..cause we did not learn the identity for the course. where u=sinx and v=e^-x...
I still havent figured this question out and its driving me nuts...please help
That is the method of "by parts" which you can readily google. There is nothing complicated with that approach; simply select the appropriate U' and dV' and be on your way. Here is another approach known as "complexifying the integral"
Evaluate the above at the given bounds to find the answer
The way to do it by parts is this
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This gives us
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Taking the limit as approaches , we get 0 because the exponential goes to 0 while the trig functions keep cycling between -1 and 1.
Plugging in 0 gives us
So in the end the integral should be 0-(-1) = 1