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Math Help - simple integral separation problem

  1. #1
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    simple integral separation problem

    If I know that:

    \frac{dk}{dl}=\frac{w}{v}

    Then does it follow that:

    dk=\frac{w}{v}dl

    \int 1 dk=\frac{w}{v}\int1dl

    \frac{k}{l}=\frac{w}{v}

    ?

    Thanks
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  2. #2
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    What variable are \displaystyle w and \displaystyle v functions of?
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by rainer View Post
    If I know that:

    \frac{dk}{dl}=\frac{w}{v}

    Then does it follow that:

    dk=\frac{w}{v}dl

    \int 1 dk=\frac{w}{v}\int1dl

    \frac{k}{l}=\frac{w}{v}

    ?

    Thanks
    You are treating w/v as though it is a constant, and you have also lost a constant of integration.

    CB
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    Yes, w/v is a constant.

    Where am I missing a constant of integration? I thought the constant of integratoin on one side cancels out with the constant of integration on the other side.
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    Grand Panjandrum
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    Quote Originally Posted by rainer View Post
    Yes, w/v is a constant.

    Where am I missing a constant of integration? I thought the constant of integratoin on one side cancels out with the constant of integration on the other side.
    What you have is:

    \displaystyle \dfrac{dk}{dl}=a

    This has solution

    k(l)=al+c

    Or to put it another way, you would have two arbitrary constants doing it your way. The sum and difference of arbitrary constants are both another arbitrary constant. That is the two constants are not equal.

    CB
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    Grand Panjandrum
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    Quote Originally Posted by rainer View Post
    Yes, w/v is a constant.

    Where am I missing a constant of integration? I thought the constant of integratoin on one side cancels out with the constant of integration on the other side.
    In that case; this is an exercise in the use of the fundamental theorem of calculus not in differential equations (so don't try to separate the variables).

    CB
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