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Math Help - Fundamental Theorem of Calculus to find the derivative of the function

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    Fundamental Theorem of Calculus to find the derivative of the function

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  2. #2
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    Firstly,

    G(x) = \int_x^6 \cos(\sqrt{2t}) dt = - \int_6^x \cos(\sqrt{2t}) dt

    The FTC says it then follows that G'(x) = -\cos(\sqrt{2x})

    Just in case a picture helps...



    ... and in this case...



    ... where straight continuous lines differentiate downwards (integrate up) with respect to x.

    Spoiler:


    __________________________________________

    Don't integrate - balloontegrate!

    Balloon Calculus: Gallery

    Balloon Calculus Drawing with LaTeX and Asymptote!
    Last edited by tom@ballooncalculus; November 20th 2009 at 10:59 AM.
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