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If we don't want to use complex analysis we can proceed in 'elementary' way first remembering that... (1) ... and that conducts to the identity... (2) ... so that is... (3) Kind regards
Last edited by chisigma; March 25th 2010 at 08:52 AM. Reason: Non decisive error corrected...
Oh , a classic integral Sub
Originally Posted by roshanhero how about x=tan(theta)??
Originally Posted by Pulock2009 how about x=tan(theta)?? Of course , anything you like could be a perfect solution ! Sub The integral becomes : Sub
Originally Posted by simplependulum Of course , anything you like could be a perfect solution ! Sub The integral becomes : Sub one more question:how do u typeout the latex so fast???
Originally Posted by Pulock2009 one more question:how do u typeout the latex so fast??? Well , most of them are copied from the previous lines , haha .
How did you get this from the above one.I am confused..
I got this answer,tell me where I am wrong
Originally Posted by roshanhero How did you get this from the above one.I am confused.. Well, that's easy- since the function being integrated is an even function, the integral from -a to a is just twice the integral from 0 to a.
Originally Posted by roshanhero I got this answer,tell me where I am wrong When i was doing the integral , i faced the same problem : The explanation is , the mapping we have taken , there is a singularity at while So we must put The substitution gives But if we do the substitution first , we will obtain which is half of the correct one .
this just comes from the fact that given and being an even integrable function on then so there's no much here, the justification comes from dealing with improper integrals.
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