# Thread: simple integral separation problem

1. ## simple integral separation problem

If I know that:

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

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

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

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

?

Thanks

2. What variable are $\displaystyle w$ and $\displaystyle v$ functions of?

3. Originally Posted by rainer
If I know that:

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

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

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

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

?

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

CB

4. 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.

5. Originally Posted by rainer
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

6. Originally Posted by rainer
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