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Integration of Q function

  1. Jan 28, 2013 #1
    can we simplify the below equation into another Q function?

    ∫0,4T(Q(2∏*(0.3) * ((t-5T/2)/(T√(ln2)))dt
    where T is a constant

    I have attached the equation in the attachements
     

    Attached Files:

  2. jcsd
  3. Jan 28, 2013 #2

    Mark44

    Staff: Mentor

    What is a Q function?
     
  4. Jan 28, 2013 #3
  5. Jan 29, 2013 #4

    lurflurf

    User Avatar
    Homework Helper

    $$\int_0^x \mathrm{Q}(t) \, \mathrm{dt}=\frac{1}{2}\int_0^x \mathrm{erfc} \left( \frac{t}{\sqrt{2}} \right) \, \mathrm{dt}=\frac{1}{2} x \, \mathrm{erfc} \left(\frac{x}{\sqrt{2}}\right)+\frac{1}{\sqrt{2 \pi}}\left(1-e^{-x^2/2}\right)= x \, \mathrm{Q} \left( x \right)+\frac{1}{\sqrt{2 \pi}}\left(1-e^{-x^2/2}\right)$$
    which can be shown by integration by parts
    your integral can then be found by change of variable
     
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