Originally Posted by

**rufi** Thanks a lot CAPTAIN for your reply. Let me write complete question :

f(x) = 1 , for |x| < a

= 0, for |x| > a

and hence find the value of INT [ { sinx/x } dx ] from 0 to infinity.

Yes, you are very right that after taking the Fourier transform of the problem, which is the same as your's, i was trying to find the inverse Fourier transform and having the difficulty in resolving this.

Could you please tell me step by step how to find inverse Fourier transform for this. The approach which i was following was :

-1

F { 2/s . sinas } = f(x)

1/2pi INT [ {2/s . sinas. e^ixs} ds] from - INF to + INF = f(x)

1/pi INT [ {1/s.sinas (cosxs +i sinxs)} ds] from -INF to + INF= f(x).

2/pi INT [ { 1/s.sinas.cosxs } ds ] from 0 to INF = f(x).

Now after this , i exactly don't know how to solve this... if we are supposed to use integration by parts, how it can be done. In a book, it solves like this after the above step :

INT [ { 1/s.sinas.cosxs} ds ] from 0 to infinity = pi/2, for |x|<a

= 0, for |x|<a

Or Forget everything and give me your way of solving this.

Thanks again CAPTAIN.