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How to do intgral for (cos(x)^2)*cos(wx)

  1. Dec 20, 2015 #1
    • Member warned about posting with no effort shown
    1. The problem statement, all variables and given/known data


    2. Relevant equations


    3. The attempt at a solution
     
  2. jcsd
  3. Dec 20, 2015 #2
    excuse me
    i want integral of cos(x^2)*cos(wx)dx
     
  4. Dec 20, 2015 #3

    Samy_A

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    I "want" that too. :smile:

    1. Are you sure that is the exercise? No typo?
    2. Please show your attempt(s) to solve the integral.
     
  5. Dec 20, 2015 #4
    actually its the Fourier cos transforms of cos(x^2)
    our teacher ask us To prove it.:headbang::headbang::headbang: i know the answer is what (see the attach file) but i want way
     

    Attached Files:

  6. Dec 20, 2015 #5

    Samy_A

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    There are probably a number of ways to prove it.

    I would start by noting that ##\cos (y)=\frac{e^{iy}+e^{-iy}}{2}##.

    But show us how you would try to find the answer, please.
    Remember that the real question is not to find the integral of ##\cos(x²)\cos(\omega x)##, but to find the Fourier transform of ##\cos(ax²)##. You could at least start by defining that Fourier transform in the "relevant equations" part of the template.
     
  7. Dec 20, 2015 #6
    thx alot
     
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