posted on Jul, 22 2005 @ 11:45 AM
Hi,
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
original equation.
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.
TheMesh
[edit on 22-7-2005 by TheMesh]