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Math Help - Antiderivative: True/False help

  1. #1
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    Antiderivative: True/False help

    I am trying to solve these set of true and false antiderivatives but cant seem to get the set right.. Can anyone point out where my concept went wrong?

    The questions is in the link
    http://img248.imageshack.us/img248/9...derivative.jpg

    1. F(x)+C, so that's false
    2. derivative = differentiate, true
    *3. F-G is anti-derivative of f-g. this one should be true. F-G can be split into 2 separate anti-derivatives, under the (addition/subtraction rule?)
    4. F'(x) = f(x) true. F is anti-derivative, and ' is derivative, so it just goes back to f
    5. f'(x) = F(x) false
    6. false, C is any arbitrary constant. making unlimited number of antiderivative
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  2. #2
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    Actually 1. is true - it doesn't matter if you add or subtract the constant.

    2. True

    3. Since the derivative/integral of a difference is equal to the difference of the derivatives/integrals, this is true.

    4. True

    5. False

    6. False, every integrable function has an infinite number of antiderivatives.


    So you got them all right except the first.
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  3. #3
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    Oh i get it. Is it because C can be either positive or negative? making the sign can be either both.
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    The wording needs work, but correct in essentials...
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  5. #5
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    Thank you for enlightening me. Sorry for the bad English, it is not my first language.
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