Re: integral of sin(x)/x

On Thu, 09 Jun 2005 08:32:52 -0400, "G. A. Edgar"
<edgar@xxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:

>In article <d89bvs$45g$1@xxxxxxxxxxxxxxxxxx>, Aloe
><Hidinginthetrees@xxxxxxxx> wrote:
>
>> Hello there
>>
>> Am trying to solve
>>
>> integral sin(x)/x dx from 0 to infinity
>>
>> i have tried substitutions z=exp(i*x) but these seem to fail because i have
>> an x at the bottom, anyone shed some light on the direction.
>>
>> i was thinking if i can compare it to a cos(x)+isin(x) problem and show that
>> cos(x) will tend to 0, leaving me with just the isin(x) part
>>
>> Thanking you in advance
>>
>>
>
>Try a contour integration, using integrand (exp(i*z)-1)/z .
>(We need the "- 1" so there will not be a singularity at z=0.)
>Now find the right contour!

With one countour we need the -1; with another countour we
don't.

Of course without the -1, using the other countour, we also
need to know the asumptotics for the integral of a function
about a small _semicircle_ centered at a pole - that's an
additional complication but a good thing to know.

************************

David C. Ullrich
.