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Proving a property of an integral

  1. Jun 23, 2012 #1
    I have already solved it, but I need confirmation:
    etfcau.jpg

    Are there other ways of proving this?

    Thanks in advance!
     
  2. jcsd
  3. Jun 23, 2012 #2

    Curious3141

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    Homework Helper

    Your proof is fine (and it's the way I would've done it), except that you should explicitly define your [itex]F(a)[/itex]. You implicitly defined it as an indefinite integral, which means [itex]F(0) = c[/itex], but I would prefer to define [itex]F(a) = \int_0^a f(x) dx[/itex], and include one more intermediary step clarifying that [itex]\int_a^{2a} f(t) dt = \int_0^{2a} f(t) dt - \int_0^a f(t) dt = F(2a) - F(a)[/itex]. This way, I don't have to bother with the [itex]F(0)[/itex] term at all.
     
    Last edited: Jun 23, 2012
  4. Jun 24, 2012 #3
    Thanks a lot!
     
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