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# C4 integration question watch

1. Hi guys,

Is anyone able to help me with this integration question from the Heinemann textbook?

I've managed to get up to here so far:

Attachment 513821513823

But I don't know where to go now

(The final answer is y^2 = 8x/(x+2))

Attached Images

2. (Original post by jasminetwine)

Hi guys,

Is anyone able to help me with this integration question from the Heinemann textbook?

I've managed to get up to here so far:

Attachment 513821513823

But I don't know where to go now

(The final answer is y^2 = 8x/(x+2))

I'm assuming you have

In which case, this gets you for some arbitrary constant , using the power rule for logarithms and "cancelling" the logs gets you

and can you then use the given information to find ?

Alternatively, you could have done: and using the power rule on which is more elegant in my opinion.
3. (Original post by Zacken)
I'm assuming you have

In which case, this gets you for some arbitrary constant , using the power rule for logarithms and "cancelling" the logs gets you

and can you then use the given information to find ?

Alternatively, you could have done: and using the power rule on which is more elegant in my opinion.
How did you get from...

To...

Attachment 513845513847

Thank you!
Attached Images

4. (Original post by jasminetwine)
How did you get from...

To...

Attachment 513845513847

Thank you!
you can write c as 0.5lnA without any loss of generality...
5. (Original post by jasminetwine)
How did you get from...

To...

Attachment 513845513847

Thank you!
It's an arbitrary constant, so I can do whatever I'd like with it - but if it makes you happy, we can do this:

since

So that I get but then you can just say without needing to bother for the sake of simplicity.

So we get once again, although you could have just as well left it in the form above if you wanted.
6. (Original post by jasminetwine)
How did you get from...

To...

Attachment 513845513847

Thank you!
Call c, 0.5 ln A and then take out the half as a common factor. Inside the bracket use the rules of logs (log a + log b = log ab and log a - log b = log a/b) to collect together the log A, log x and - log |x+2| into one log.

The trick of changing c to log k is very common in doing the algebra in tidying up solutions of DEs
7. Alternatively, you could plug in your conditions for y, x right away from to find - if that makes you more comfortable.

Here are my workings, if anybody is interested!

Thanks again!

Have a lovely weekend everybody!
9. (Original post by jasminetwine)
First class work.

Which do you think is your favourite method?

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