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Thread: 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 $\displaystyle C(x)$ to find $\displaystyle C'(x)$, if

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

    where $\displaystyle N_j$ is some constant, and $\displaystyle k(s)$ 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 $\displaystyle C(x)$ to find $\displaystyle C'(x)$, if

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

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

    RonL
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  3. #3
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    Would $\displaystyle C'(x)$ be

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

    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; Sep 15th 2007 at 02:49 PM.
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  4. #4
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    Can anyone check my work?

    Thanks
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