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Thread: Multiple solutions in antidifferentiation.

  1. #1 Multiple solutions in antidifferentiation. 
    Forum Junior epidecus's Avatar
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    Aug 2012
    When you were first taught about finding antiderivatives and indefinite integration, the instructor probably mentioned the catch about there being more than one solution. Always remember that "plus C" at the end, because the derivative of a constant is zero. But disregarding this constant, all the solutions are pretty much the same. Right? Or no?

    That's my question. Could a function have more than one antiderivative where the main function itself is different, instead of just the constant being different? Probably a stupid question, but I'm really not sure because I'm reviewing stuff from calculus... And when I was taught this, I sort of felt that the instructor was hinting that there was more to the catch. But I don't really remember him explicitly addressing this. So answers are much appreciated.

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  3. #2  
    Forum Ph.D.
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    Jul 2008
    New York State
    Let h = f - g. Since f' = g', then h' = f' - g' = 0. When you integrate 0, you get a constant, that is h is a constant, so f - g = h is constant.

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