Edexcel maths A level paper 2 sample

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cata03
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I’m doing question 16 on the edexcel paper 2 sample paper and it integrates 4/(11-2P) dP to -2ln(11-2P).

I thought that it would integrate to 4ln(11-2P). Don’t know if I’m missing something really obvious here??
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gdunne42
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(Original post by cata03)
I’m doing question 16 on the edexcel paper 2 sample paper and it integrates 4/(11-2P) dP to -2ln(11-2P).

I thought that it would integrate to 4ln(11-2P). Don’t know if I’m missing something really obvious here??
try differentiating 4ln(11-2P) and what do you get?
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cata03
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(Original post by gdunne42)
try differentiating 4ln(11-2P) and what do you get?
Ah yes i see where I went wrong now! Is there a technique you can use to integrate 4/(11-2p) or did you just do it by inspection?
thanks so much!
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Notnek
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(Original post by cata03)
Ah yes i see where I went wrong now! Is there a technique you can use to integrate 4/(11-2p) or did you just do it by inspection?
thanks so much!
Substitution u=11-2p would also work.
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gdunne42
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(Original post by cata03)
Ah yes i see where I went wrong now! Is there a technique you can use to integrate 4/(11-2p) or did you just do it by inspection?
thanks so much!
Yes I'd generally do these by inspection.
Love that word 'inspection' makes it sound much more respectable than take an educated guess and see what is wrong with your guess and tweak it.
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2ms7osnsi
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(Original post by cata03)
Ah yes i see where I went wrong now! Is there a technique you can use to integrate 4/(11-2p) or did you just do it by inspection?
thanks so much!
integral(f’(x)/f(x)) = ln(f(x))

Good formula to know for all fraction integrals

so just rearrange it to a form where it’s a constant multiplier * f’(x)/f(x), in this case -2 * (-2/11-2p) and integrate!

Specific easy to remember case of this for linear denominator and constant numerator: integral(a/bx+d) = a/b ln(bx+d)
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