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# Core 4 integration Watch

1. The voluem of liquid Vcm^3 at time t seconds satisfies

-15DV/dt = 2V - 450

Given that initially the volume is 300cm^3, find tot he nearest cm^3 the volume after 15 seconds.
2. (Original post by Claxxy)
The voluem of liquid Vcm^3 at time t seconds satisfies

-15DV/dt = 2V - 450

Given that initially the volume is 300cm^3, find tot he nearest cm^3 the volume after 15 seconds.
What are you stuck with in particular? Do you know the separation of variables method?
3. Not really
We haven't been taught this section properly
4. (Original post by Claxxy)
Not really
We haven't been taught this section properly
The way the method works is:

First you rearrange the equation so that (roughly speaking) everything involving V appears on the same side as , and everything involving t appears on the other side. So what you you get should look something like

For some functions f and g.

Once you have this, the next step is:

To get to this step, you can visualise bringing the over to the right-hand side of the equation and integrating both sides. This isn't acutally what happens, but it's what I was taught at A level and seems like a good way to make sense of the method.*

Now you can just evaluate these two integrals as usual (remembering a constant of integration), and apply the initial conditions.

*If you're interested, at this point we're actually integrating both sides with respect to t.

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Updated: December 12, 2010
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