posted on Jul, 22 2005 @ 11:45 AM
No idea where you are going with this, must be just a fun time waster.
I originally by looking at it thought it would involve Euler's formula, but I think I was off track. I believe the correct solution involves
integration by parts... Done twice.
It is a long detail, anyone can look up the formula for integration by parts, but start off by using e^2x as your u', and sin(x) as the v. Perform
the calculations. You end up with uv - integral of uv'.
Perform the integration by parts on the second term.... and use artihmetic, you will come up with the following equality for the left term in your
e^2x/3 [2sin(x)] - cox(x)] evaluated at pi/2 and 0.
I come up with the ultimate answer of (2e^pi + 1) / 3.
Tell me if I have gone wrong, or if you are just testing. I am off by a small factor from your answer.
I can also detail the proof, maybe in a web link. It might be better to do it this way, to give someone else a hint on the solution.
[edit on 22-7-2005 by TheMesh]