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Integral and differential of summation

  1. May 15, 2014 #1
    The following identities are true?
    $$\frac{d}{dx} \sum_{u_0}^{u_1}f(x,u)\Delta u = \sum_{u_0}^{u_1}\frac{d}{dx}f(x,u)\Delta u$$ $$\int \sum_{u_0}^{u_1}f(x,u)\Delta u dx = \sum_{u_0}^{u_1}\int f(x,u)dx\Delta u$$
     
  2. jcsd
  3. May 15, 2014 #2

    HallsofIvy

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    As long as [itex](u_1- u_0)/\Delta x[/itex] is finite, those can be proved by induction.
     
  4. May 15, 2014 #3
    I didn't understand...
     
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