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Homework Help: Weird integration problem.

  1. Oct 20, 2006 #1
    Here I am, asking yet another question. :), Gotta keep you guys busy you know.

    I am just practicing a bunch of integration questions found in a textbook a friend lent me, and I probably don't need to know how to integrate this, but I am interested anyways :).

    [tex]\int_{0}^{0.5}\frac{dx}{\sqrt{1-x^{2}}}[/tex]

    This looks like a "Do you understand the notation", type question to me. I don't need help integrating, but only finding an antiderivative, I think I can handle the rest.

    Is this some fancy way of writing [tex]\int_{0}^{0.5}\frac{1}{\sqrt{1-x^2}}dx[/tex]? As this would normally be the way I would expect to see it. Or is it different? If it's what I think it is then of course the antiderivative is simply [tex]sin^{-1}x[/tex] , but I want to make sure. It's an even numbered question so there is no answer in the back :(.

    Thanks yet again.
     
  2. jcsd
  3. Oct 20, 2006 #2

    arildno

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    Yes, it means the same thing, just imagine "dx" as a number (even if it isn't, really). Then that new way of writing "follows" (even if it doesn't, really).

    conclusion:
    Just another notational convenience.
     
  4. Oct 20, 2006 #3
    Okay, thanks again.
     
  5. Oct 20, 2006 #4

    HallsofIvy

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    You do understand, do you not, that you are asking if [itex]\frac{a}{b}[/itex] is a "fancy" way of writing [itex]\frac{1}{b}a[/itex]?
     
  6. Oct 20, 2006 #5
    Well, I don't understand dx as being a "number" or a "unit" or anything like that in the case of integral notation. I figured that it meant that, but was not 100% sure. I could have assumed that common sense applies, but I could have been wrong right? I think that it's better to check then to assume, esspecially when learning new mathematical notation.
     
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