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1. C4 Integration and Differentiation
I never know what certain things integrate/differentiate into, for example tanx and stuff, I also don't even know what we need to know how to integrate or differentiate. I'm ok with all the different types off methods but within them I just get so confused with things such as ln, things with fractions or tans and secs etc. So does anyone have a list of things we need to know how to integrate/differentiate for C4, because I'm sure my C4 textbook doesn't include them all!
Thank you.
2. Re: C4 Integration and Differentiation
I'll try and do the best I can - C4 Differentiation and Integration is like saying just C4, because that's all it really is!

First of all, tan x is given in your formula book which you get in the exam. Tan x integrates to Ln ¦sec x¦

To differentiate tan x, you just break it down => tan x = (sin x / cos x) = sin x . (1/cos x) = sin x sec x

There are certain rules to learn - one of them is that sec x differentiates to sec x tan x - you just have to memorise these. They should be at the end of the chapter from your C3 book?

You have to use the product rule to differentiate tan x, but you can just learn the result: (Sec x)^2

When you have to integrate a complex looking fraction, more often than not this will be a combo Partial fractions + integration question. Once you separate the fraction into the form a/f(x) + b/g(x), you just use the Ln integration rule:

Integral of (1/ax+b) dx = 1/a Ln ¦(ax+b)¦ + C

This is a standard generalisation - again they are at the end of the topic, and you just have to learn them.

Which C4 textbook are you using? I can always scan in the summary page from my one if you want - I used to just keep it by my side when answering integration questions, until the rules just came to me by memory.
3. Re: C4 Integration and Differentiation
(Original post by Chronoscon)
First of all, tan x is given in your formula book which you get in the exam. Tan x integrates to Ln ¦sec x¦

To differentiate tan x, you just break it down => tan x = (sin x / cos x) = sin x . (1/cos x) = sin x sec x ... ... ... You have to use the product rule to differentiate tan x, but you can just learn the result: (Sec x)^2

Integral of (1/ax+b) dx = 1/a Ln ¦(ax+b)¦ + C
Do not know what board you are doing but aren't all of the above in the formula book

(Original post by Chronoscon)
There are certain rules to learn - one of them is that sec x differentiates to sec x tan x - you just have to memorise these.
Why memorise this rather than others

Easy to do with the chain rule
4. Re: C4 Integration and Differentiation
(Original post by Chronoscon)
I'll try and do the best I can - C4 Differentiation and Integration is like saying just C4, because that's all it really is!

First of all, tan x is given in your formula book which you get in the exam. Tan x integrates to Ln ¦sec x¦

To differentiate tan x, you just break it down => tan x = (sin x / cos x) = sin x . (1/cos x) = sin x sec x

There are certain rules to learn - one of them is that sec x differentiates to sec x tan x - you just have to memorise these. They should be at the end of the chapter from your C3 book?

You have to use the product rule to differentiate tan x, but you can just learn the result: (Sec x)^2

When you have to integrate a complex looking fraction, more often than not this will be a combo Partial fractions + integration question. Once you separate the fraction into the form a/f(x) + b/g(x), you just use the Ln integration rule:

Integral of (1/ax+b) dx = 1/a Ln ¦(ax+b)¦ + C

This is a standard generalisation - again they are at the end of the topic, and you just have to learn them.

Which C4 textbook are you using? I can always scan in the summary page from my one if you want - I used to just keep it by my side when answering integration questions, until the rules just came to me by memory.
it's not even a textbook, all i've got is some rubbish revision guide! yessss that would be great please! and i've finished C3 so haven't got the book any more, so if you scan that, that for me it would be great! thank you sooo much
5. Re: C4 Integration and Differentiation
(Original post by examssuck.)
it's not even a textbook, all i've got is some rubbish revision guide! yessss that would be great please! and i've finished C3 so haven't got the book any more, so if you scan that, that for me it would be great! thank you sooo much
Heres scans of everything - the sheets with Core Mathematics C4 and Core Mathematics C3 at the top are formula sheets given to you in the exam (at least for my board - Edexcel), so you don't need to memorise them, more just know how to apply them.

The textbook scans are pretty generic no matter what the board is. They include stuff from C3 and C4 - all of which has to be memorised.

Hope this helps!