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Change of integral variable

  1. Aug 11, 2016 #1
    1. The problem statement, all variables and given/known data
    I want to change integral variable to jx it means (w=jx)
    9355588700_1470901837.png

    2. Relevant equations


    3. The attempt at a solution
    3381303200_1470901807.jpg
    but as you see the bounds of integral are different from the book text , what is my mistake?
     
  2. jcsd
  3. Aug 13, 2016 #2

    Simon Bridge

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    hat about the part that says: "by using the Cauchy theorem and showing that..."?
     
  4. Aug 14, 2016 #3
    dear Simon
    I didn't understand how can I use the Cauchy tip to solve this inconsistency?
     
  5. Aug 14, 2016 #4

    Simon Bridge

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    It's a step you seemto have left out though.
    I'll agree it looks like there's a minus sign missing. Maybe there's a typo? I can't actually read the image properly.
     
  6. Aug 14, 2016 #5

    pasmith

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    It allows you to perform the integral from [itex]\omega = -i\infty[/itex] to [itex]\omega = +i\infty[/itex], which on setting [itex]\omega = ix[/itex] becomes [itex]x = -\infty[/itex] to [itex]x = \infty[/itex].
     
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