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Homework Help: Using Fourier Transforms to solve Definite Integrals with Limits 0 to Infinity

  1. Mar 8, 2010 #1
    1. Using Fourier Transforms to solve Definite Integrals with Limits 0 to Infinity

    I'm trying to understand how to use Fourier Transforms to solve Definite Integrals with limits from 0 to Infinity.
    I understand how to use Fourier Transforms to solve indefinite integrals, but I believe there is supposed to be a much simpler way to solve these definite integrals without working out the entire indefinite solution.


    2. Relevant equations
    X(j0) = Integral from -Infinity to Infinity : x(t)dt
    x(0) = Integral from -Infinity to Infinity: X(jw)dw
     
  2. jcsd
  3. Mar 8, 2010 #2

    marcusl

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    Welcome to PF! Here's a hint: Think about even and odd time functions.
     
  4. Mar 8, 2010 #3
    [tex]\displaystyle\int^\infty_0 2te^-^a^t\cos(t)\,dt = ?}[/tex]

    I'm not entirely sure how to manipulate this.. the [tex]e^-^a^t[/tex] makes it so the function is neither even nor odd anymore.. even if I pulled the even part out to rewrite the function so its integrated from -infinity to infinity I'm unsure about what to do with the odd piece.
     
  5. Mar 8, 2010 #4

    marcusl

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    Yikes! I don't know what to do with this either. Sorry I jumped in...
     
  6. Mar 8, 2010 #5
    I appreciate the thought! Thanks! :)
     
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