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Integral with only one limit of integration?

  1. Jan 20, 2007 #1
    1. The problem statement, all variables and given/known data
    Work it out with pencil and paper.
    [tex] \int^x \frac{x'dx'}{1+x'^2} [/tex]


    2. Relevant equations
    none


    3. The attempt at a solution
    My only question is what does it mean to have only one limit of integration? I am used to doing integrals in the indefinite case with no limits of integration, or in the definite case with two limits of integration.

    What does this single limit of integration mean, and what do I do with it? Do I assume 0 for the other limit? Do I just solve it as a an indefinite integral?

    Thanks for any clues!


    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited: Jan 20, 2007
  2. jcsd
  3. Jan 20, 2007 #2

    cristo

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    I've never seen that notation before! I'd say you just integrate it indefinitely, then substitute x in for x'.
     
  4. Jan 20, 2007 #3
    Yeah, I'd say set the bottom limit equal to 0 so that it makes the second part of the solution disappear.
     
  5. Jan 20, 2007 #4

    HallsofIvy

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    The notation [itex]\int^x f(x')dx'[/itex] is just an indefinite integral. Remember that the variable inside the integral is a "dummy" variable- the "x" as a limit of integration just tells you what variable to use in the resulting function.

    Do NOT set the bottom limit to 0! That is not justified.
     
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