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Math Help - Antidifferentiation problem

  1. #1
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    Antidifferentiation problem

    If f(x) = (x+1)^2 and F(1) = 2, find F(x).

    I can't get the answer. Could someone explain to to me? And also, what is the difference between f(x) and F(x)??

    Thank you for your help.
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  2. #2
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    I assume that F(x) is the antiderivative of f(x).

    So if f(x) = (x + 1)^2 = x^2 + 2x + 1 then

    F(x) = \int{x^2 + 2x + 1\,dx}

     = \frac{1}{3}x^3 + x^2 + x + C.


    You know that F(1) = 2, so

    2 = \frac{1}{3}(1)^3 + 1^2 + 1 + C

    2 = \frac{1}{3} + 1 + 1 + C

    2 = \frac{7}{3} + C

    C = -\frac{1}{3}.


    Therefore F(x) = \frac{1}{3}x^3 + x^2 + x - \frac{1}{3}.
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  3. #3
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    thanks!!
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