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Fourier cosine integral

  1. Sep 16, 2012 #1
    1. The problem statement, all variables and given/known data
    show that
    xf(x)=integral from 0 to infinity of [B*(w)sin(wx)]dw , // B* is a function not B * w

    where B* = -dA/dw
    A(w) = 2/pi integral from 0 to infinity [f(v) cos(wv)] dv

    2. Relevant equations


    f(x)=integral from 0 to infinity [A(w)cos(wx)] dw
    3. The attempt at a solution

    working on right hand side
    B*= 2/pi * integral from 0 to infinity [vf(v)cos(wv)dv]
    =integral from 0 to infinity of [2/pi * integral from 0 to infinity [vf(v)cos(wv)dv]sin(wx)]dw
    left side = integral from 0 to infinity [ A(w)xcos(wx)]dw

    Even when i tried writing A as integral i dont see how do i prove 2 sides which have 2 integrals in them equal each other?
     
  2. jcsd
  3. Sep 16, 2012 #2
    >_> I know I didn't do alot of work but there is not much to work on from the book and I don't really know how to algebriacly manipulate integrals of the form g(x) = integral from 0 to infinity f(x,y)dy
     
  4. Sep 16, 2012 #3
    should I repost this in engineering section?
     
  5. Sep 17, 2012 #4
    those are pictures of the problem if it's not clear ><

    (20)(a2)
     

    Attached Files:

    Last edited: Sep 17, 2012
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