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Average of 2 functions

  1. Nov 2, 2011 #1
    1. The problem statement, all variables and given/known data
    My question pertains to taking the average over a particular period that is composed of 2 functions. For example, from [0, 5ms] the function is defined by 1-e^(-t/1ms)and then by e^(-t/1ms) from [5ms, 10ms].

    Will the average from 0-->10 simply be the following:
    [tex]\bar{f}=\frac{1}{5}\int^{5 ms}_{0}{1-e^{-t/1 ms}}+\frac{1}{5}\int ^{5}_{0}{e^{-t/1 ms}}[/tex]
     
  2. jcsd
  3. Nov 2, 2011 #2
    If you look at the bottom graph that is orange, it gives visual representation as to what I am trying to take the average of. One period, two functions. One function for half the period, another function for the last half.
    1873_8RC%20Input%20Waveform.JPG
     
  4. Nov 3, 2011 #3
    Nvm, pretty sure it is as follows:
    [tex]\bar{f}=\frac{1}{10}\int^{5 ms}_{0}{1-e^{-t/1 ms}}+\frac{1}{10}\int ^{5}_{0}{e^{-t/1 ms}}[/tex]
    Since the entire period is 10, then both contributions from each function needs to be divided by this number. If I hadn't done this, I would not be considering the other half where each function is zero.
     
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