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Integral Properties

  1. Feb 6, 2008 #1
    Last edited: Feb 7, 2008
  2. jcsd
  3. Feb 6, 2008 #2
    Differentiation and integration are inverse operations.
  4. Feb 6, 2008 #3
    yep, the integral of f'(x)dx is simply f(x).
  5. Feb 6, 2008 #4
    oh ok I see, so then it is just e ^ (tan^-1(x)) ?
  6. Feb 6, 2008 #5
    +C, do not forget the constant, sometimes it can be really painful if you forget to add a constant at the end.
  7. Feb 6, 2008 #6
    Oh ok, also do I evaluate that function over the interval [a,b] then? I forgot to mention it before.
  8. Feb 6, 2008 #7
    Are u taking the indefinite or definite integral of that function? Why don't you show the original question first? it usually makes it easier for everyone!
  9. Feb 7, 2008 #8

    Gib Z

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    Theres really no such thing as an indefinite integral =] Its just commonly used shorthand notation.

    [tex]\int f(x) dx[/tex] really means [tex]\int^x_a f(t) dt[/tex] where a is some constant.
  10. Feb 7, 2008 #9


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    No, it doesn't. [tex]\int f(x) dx[/tex] is any anti-derivative of f- it involves an arbitrary constant. The "a" in [tex]\int_a^x f(x) dx[/tex] determines a specific constant.
  11. Feb 7, 2008 #10
    yep, just evaluate it over the interval [0,1]
  12. Feb 8, 2008 #11

    Gib Z

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    [tex]\int^x_a f(t) dt[/tex] plus an arbitrary constant then =]
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