A LevelMathsOCRMaths APureRevision NotesIntegrationFurther IntegrationReverse Chain Rule

Reverse Chain Rule (OCR A Level Maths A) : Revision Note

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Paul

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OCR Maths A: PureAQA Maths: PureEdexcel Maths: Pure

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Reverse Chain Rule

What is the chain rule?

  • The Chain Rule is a way of differentiating two (or more) functions

Notes cr, AS & A Level Maths revision notes

  • In many simple cases the above formula/substitution is not needed

Notes cr_egs, AS & A Level Maths revision notes

  • The same can apply for the reverse – integration

Integrating with reverse chain rule

Notes rcr_egs, A Level & AS Level Pure Maths Revision Notes

  • In more awkward cases it can help to write the numbers in before integrating

  • STEP 1: Spot the ‘main’ function

  • STEP 2: ‘Adjust’ and ‘compensate’ any numbers/constants required in the integral

  • STEP 3: Integrate and simplify

Notes num_adj1, A Level & AS Level Pure Maths Revision Notes
Notes num_adj2, AS & A Level Maths revision notes

Examiner Tips and Tricks

  • If in doubt you can always use a substitution.

  • Differentiation is easier than integration so if stuck try the opposite, eg. sin and cos are linked (remember that minus!) so if integrating a sin function, start by differentiating the corresponding cos function.

  • Lastly, check your final answer by differentiating it.

Worked Example

Example soltn(a), AS & A Level Maths revision notes
Example soltn(b), AS & A Level Maths revision notes
Example soltn(c), AS & A Level Maths revision notes
Example note, AS & A Level Maths revision notes
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Paul

Author: Paul

Expertise: Maths Content Creator (Previous)

Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams.

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