If I know that:

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

Then does it follow that:

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

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

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

?

Thanks

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- Feb 18th 2011, 10:38 PMrainersimple integral separation problem
If I know that:

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

Then does it follow that:

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

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

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

?

Thanks - Feb 18th 2011, 10:41 PMProve It
What variable are $\displaystyle \displaystyle w$ and $\displaystyle \displaystyle v $ functions of?

- Feb 18th 2011, 10:49 PMCaptainBlack
- Feb 18th 2011, 10:56 PMrainer
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. - Feb 18th 2011, 11:57 PMCaptainBlack
What you have is:

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

This has solution

$\displaystyle k(l)=al+c$

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 - Feb 18th 2011, 11:59 PMCaptainBlack