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Simple Integration problem

  1. Sep 1, 2009 #1
    This isn't a homework question, just something I was wondering about, and this seemed like the most appropriate place to post it because of its simplicity.

    When integrating a function of the form f(x)=(x-a)[tex]^{n}[/tex], I find I get a different result if I expand the brackets first and then integrate.

    Example:
    [tex]\int[/tex]2(x-5)dx = (x-5)[tex]^{2}[/tex] + C = x[tex]^{2}[/tex]-10x-25 + C
    [tex]\int[/tex]2x-10dx = x[tex]^{2}[/tex]-10x + C

    I was wondering if the C in the first equation will simply just be 25 greater than the C in the second equation, or is there more to it than that?

    Thanks for your time,
    Andrew
     
  2. jcsd
  3. Sep 1, 2009 #2

    rock.freak667

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    Homework Helper

    In your two integrals, the values of 'C' are different. In the first one you have -25 + C, which is in itself another constant k. So you can rewrite it as x2 -10x+k. Which is in the same form as your second integral.
     
  4. Sep 1, 2009 #3
    Thanks rock.freak667!
     
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