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How do i show this integral equals zero? (I'm quite positive it does)

  1. Jan 25, 2014 #1
    1. The problem statement, all variables and given/known data
    So on my first day of intro to quantum physics my teacher assigned a lot of calculus problems as homework. One of them problems was a quite lengthy proof that one integral is the equivalent of another, and I am so close to getting the correct answer!!

    All I need to do to finish my proof is to show that the integral

    integral: ((sin(ax)sin(bx))/x) dx between -inf and inf is equal to zero.
    I'm having trouble doing this.. help?
    I've tried using the trig identity to turn sin(ax)sin(bx) into 1/2(cos(ax-bx) + cos(ax+bx)) but still feel the integral is above my capabilities.. i'm not suppose to use wolfram alpha or such things.


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 25, 2014 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Use the symmetry of the integrand. What happens if you replace x with -x?
     
  4. Jan 25, 2014 #3

    jedishrfu

    Staff: Mentor

    If you were to plot it and then visually inspect it you'd see whether you were right about it being zero then following Dick's advice yo'd be able to prove it.
     
  5. Jan 25, 2014 #4
    ahh it's an odd function!! I kept thinking it's an even function but completely forgot to include the x on bottom! Thanks you guys are f'n smart!
     
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