How to simplify "Integrate[2 f[x], {x, 0, 1}]/2" to "Integrate[f[x],

Discussion in 'Mathematica' started by Klaus Engel, Apr 16, 2010.

  1. Klaus Engel

    Klaus Engel Guest

    Dear group,

    I tried to simplify an awkward looking integral with "Mathematica 7"
    using its "(Full)Simplify[...]" function. Unfortunately it failed to do
    so, even though I know that this would be possible. I boiled down the
    problem to the following very simple example ("f" is just a generic,
    undefined function): The input

    Integrate[2 f[x], {x, 0, 1}]/2 // FullSimplify

    returns just the input

    Integrate[2 f[x], {x, 0, 1}]/2

    (same result for "Simplify" instead of "FullSimplify"), i.e.,
    Mathematica seems not to be aware that the factor "2" can be canceled
    out. Even worse, the expressions

    TrueQ[Integrate[2 f[x], {x, 0, 1}]/2 == Integrate[f[x], {x, 0,
    SameQ[Integrate[2 f[x], {x, 0, 1}]/2 , Integrate[f[x], {x, 0, 1}]]
    Integrate[2 f[x], {x, 0, 1}]/2 === Integrate[f[x], {x, 0, 1}]

    return the (wrong) result "False".

    So my question: Is there something I am overlooking, or what is the
    right "Mathematica" way to treat expressions like the one above.

    Thanks a lot in advance,

    Klaus Engel, Apr 16, 2010
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  2. Hi Klaus

    Why do you assume that Integrate[2 f[x], {x, 0, 1}] exist ?
    (Assume i.e. f[x] has a pole at 1)

    It seems to me that mathematica is not shure about this and so
    it leaves the intgral expression untouched.

    What happens when you define f[x] ?

    Just my $0.01
    Andreas Hinze, Apr 17, 2010
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