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Math Help - integration constant

  1. #1
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    integration constant

    why do we put arbitrary constant in integration
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  2. #2
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    Differentiate these functions

    y_1 = x^2+10x+7

    y_2 = x^2+10x-9

    y_3 = x^2+10x+2

    What do you get? What does this mean?
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  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
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    Hey there...

    It's...
    The fundamental theorem of calculus:


    F(x)=\int_a^x{f(t)dt}
    where f is a real-valued function continuous on [a, b]. Then, F is continuous on [a, b], differentiable on the open interval (a, b), and:
    F'(x)=f(x)  \\\\  \forall x \in (a,b)
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  4. #4
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    Quote Originally Posted by prasum View Post
    why do we put arbitrary constant in integration
    Say you want to integrate f(x) = x^2. Writing \int{2x}\;{dx} = x^2 means to say that the function f(x) = 2x satisfies F'(x) = x^2. But is it the only one that satisfies this relation? Clearly, 2x+1 satisfies; so do 2x+2 and 2x+3. In fact, for any number C, it's true that 2x+C satisfies the relation. Finding \int{f(x)}\;{dx} means finding the set of all function which satisfy F'(x) = f(x), i.e the set of all anti-derivatives of f(x).
    Last edited by TheCoffeeMachine; May 25th 2010 at 06:35 PM.
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  5. #5
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    Quote Originally Posted by TheCoffeeMachine View Post
    Writing \int{x^2}\;{dx} = 2x
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  6. #6
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    Quote Originally Posted by pickslides View Post
    . Thank you.
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