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Integrating one variable with respect to another

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?

Reply 1

Oh I Really Don't Care

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.

Reply 2

SCE1912

Its v a known function of t. If so substitute that in.

If you are trying to solve the differential equation

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

Then you must seperate your variables before integrating

Reply 3

shawrie777

That is what i'm trying to do SCE1912 I think I've done it now.
Is the solution

t = \frac{m}{kv}+c

Reply 4

Oh I Really Don't Care

you need a minus

Reply 5

shawrie777

oh yeah got it now thanks guys

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Integrating one variable with respect to another

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