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Math Help - Fundamental Theorem of Calculus Part 2

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    Member Chokfull's Avatar
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    Fundamental Theorem of Calculus Part 2

    Can anyone help me understand this?

    The FTC1 says, basically, that an integral of a function equals the antiderivative of that function, or

    If f is continuous on [a, b], then the function g defined by

    g(x) = \int_a^xf(t)dt a\le x\le b
    is continuous on [a, b] and differentiable on (a, b), and g'(x) = f(x).
    However, the FTC2 says that \int_a^bf(x)dx=F(b) - F(a), where F is the antiderivative of f.

    But why would it be the difference between two antiderivatives rather than just being an antiderivative in itself?
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    Quote Originally Posted by Chokfull View Post
    Can anyone help me understand this?
    The FTC1 says, basically, that an integral of a function equals the antiderivative of that function, or
    However, the FTC2 says that \int_a^bf(x)dx=F(b) - F(a), where F is the antiderivative of f.
    But why would it be the difference between two antiderivatives rather than just being an antiderivative in itself?
    What exactly does that question mean?
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    Member Chokfull's Avatar
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    Never mind i realized I was being stupid :P
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