Help wanted
Please post a solution for :
∫(sin3x/x) dx
It is not a non-integratable function so keep trying.
∫(sin3x/x) dx
It is not a non-integratable function so keep trying.
posted by Prateek at 10:03 PM
Place to discuss and solve some of the best questions.
posted by Prateek at 10:03 PM
7 Comments:
This is basically a scaled sinc function, whose fourier transform is a rect (a square wave). If you want to calculate a finite-interval integral for the expression (say from a to b), it amounts to caculating the integral (from minus infinity to infinity), of the expression multiplied by a shifted square wave. Multiplication in time domain is convolution in frequency domain - so your final answer is basically the value of the fourier transform of sin3x/x * rect(2*(t-(b+a)/2)/(b-a)) evaluated at f = 0. Simple, isn't it ?
The person who has posted this message can you please identify yourself
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I tried it on a software called Mathematica 5 and what I get is that the answer is:
SinIntegral(3x)
where SinIntegral is the function defined as a definite integral:
Si(z) = ∫ (sinx)dx/x, from 0 to z
This seemingly is very similar to your function, the only difference being that it has limits.
It also says that "SinIntegral of z is the entire function of z with no branch discontinuities."
Now, I must be honest in the fact that this whole thing has just flown over my head, except for one fact that perhaps sinx/x is not a perfectly integrable function. I've posted this information incase people here, who are by and large more intelligent than me, can figure it out.
Well it is an integral function and that I am sure of, and I was also told, by the person who gave me this question that it involves a little trick, but I did confirm that it was not some stupid trick but an intelligent and quite logical one, so keep trying.
Look buddy, I don't know what mad mathematician friends you've made, but when Mathematica can't integrate something, that's where I give up hope too.
I haven't made any mathematecian friends, its just a challenge given to me by the man [a flight inspector] sitting next to me on my flight from Delhi to Chennai.
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