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Math Help - Antiderivative Question

  1. #1
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    Antiderivative Question

    If f(x) = 4x - e - 0.5 x, and F(x) is an antiderivative function of f(x) with F(0) = 3, which of the following equals F(3) rounded off to two decimal places?

    The answer is 19.45

    When I worked it out, I got 17.54, which is not right. Could someone explain? Thanks.
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  2. #2
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    Hello vease1999
    Quote Originally Posted by vease1999 View Post
    If f(x) = 4x - e - 0.5 x, and F(x) is an antiderivative function of f(x) with F(0) = 3, which of the following equals F(3) rounded off to two decimal places?

    The answer is 19.45

    When I worked it out, I got 17.54, which is not right. Could someone explain? Thanks.
    I assume you mean:
    f(x) = 4x -e^{-0.5x}
    in which case:
    F(x) = 2x^2+2e^{-0.5x}+c

    F(0) = 2+c = 3

    \Rightarrow c = 1
    \Rightarrow F(3) = 18 + 2e^{-1.5}+1
    = 19.45 (2 d.p.)
    Grandad
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