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Math Help - Second Fundamental Theorem of Calculus

  1. #1
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    Second Fundamental Theorem of Calculus

    Is it possible to use the Second Fundamental Theorem of Calculus on C(x) to find C'(x), if

    C(x)=\sum_{j=1}^{n}{\bigg|N_{j}\int_{x}^{x_j}{k(s)  ds}\bigg|} ,

    where N_j is some constant, and k(s) is integrable over every interval?
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  2. #2
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    Quote Originally Posted by Fourier View Post
    Is it possible to use the Second Fundamental Theorem of Calculus on C(x) to find C'(x), if

    C(x)=\sum_{j=1}^{n}{\bigg|N_{j}\int_{x}^{x_j}{k(s)  ds}\bigg|} ,

    where N_j is some constant, and k(s) is integrable over every interval?
    Yes

    RonL
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  3. #3
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    Would C'(x) be

    C'(x)=\sum_{j=1}^{n}{\bigg|N_j k(x_j)\bigg|} \textrm{ ?}

    If this is correct, then it implies that the derivative is always nonnegative and increasing as the sum increases from 1 to n.
    Last edited by Fourier; September 15th 2007 at 03:49 PM.
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  4. #4
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    Can anyone check my work?

    Thanks
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