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Integrating one variable with respect to another

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    Hi I need to calculate this:

     \int \frac{k}{m}v^2 \, dt

    Where V and t are variables and k and m are constants. I don't know how to go about this with there being a second variable. Can anyone help?
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    velocity is the first derivitive of displlacement with respect to time.

    ... perhaps if you gave the entire question we may be able to help - integrating squares of derivitives is diffcult in most cases.
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    Its v a known function of t. If so substitute that in.

    If you are trying to solve the differential equation


\displaystyle \frac{dv}{dt} = \frac{k}{m}v^2

    Then you must seperate your variables before integrating
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    That is what i'm trying to do SCE1912 I think I've done it now.
    Is the solution  t = \frac{m}{kv}+c
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    you need a minus
  6. Offline

    oh yeah got it now thanks guys


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Updated: March 1, 2009
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