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Integral of [sinx * sin(x^2)]

  1. Dec 25, 2012 #1
    I've never cracked this 1 yet, and I don't remember if it's domain was [0,1] or [0,∞), pretty sure it was 1 of the 2, and not anything with -∞ or ∏/2 for example

    ∫[sinx * sin(x^2)]dx
  2. jcsd
  3. Dec 25, 2012 #2

    Simon Bridge

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  4. Dec 25, 2012 #3


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    sin(x)* sin(x^2)=[sin((x-1/2)^2)-sin((x+1/2)^2)]sin(1/4)/2+[cos((x-1/2)^2)-cos((x+1/2)^2)]cos(1/4)/2

    Your integral is then easily expressed in terms ofFresnel integrals. As far as what limits make the answer tidy, probably none.
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