A LevelMaths: Pure 3CIERevision Notes5. Integration5.1 Further Integration5.1.8 Integration Decision Making

Integration Decision Making (CIE A Level Maths: Pure 3)

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Decision Making

What is meant by integration and decision making?

  • The hardest part of integration is deciding which technique to use
  • There are lots of them!

Notes meth_mess, downloadable AS & A Level Maths revision notes

How do I know which integration method to use?

Notes int_2main, downloadable AS & A Level Maths revision notes

  • The main two requirements for success with integration are
    • Experience
    • Familiarity
  • Always check for Reverse Chain Rule …
    • … particularly after changing part of an integral …
    • … by using a trig identity for example

 Notes int_flow, downloadable AS & A Level Maths revision notes

Key to diagram above:

(1) Powers of x   

(2) Substitution

(3) Obvious substitution   

(4) Trig

(5) Algebraic Division   

(6) fraction numerator straight f apostrophe left parenthesis x right parenthesis over denominator straight f left parenthesis x right parenthesis end fraction

(7) Partial fractions   

(8) Integration by Parts

(9) Reverse Chain Rule

Examiner Tip

  • If in doubt, try something … You may gain marks for attempting a suitable substitution.
  • You may gain marks from using a trig identity.
  • You may gain marks from attempting to simplify or rewrite a fraction.

Worked example

Example soln_a, downloadable AS & A Level Maths revision notesExample soltn_b, downloadable AS & A Level Maths revision notesExample soltn_c, downloadable AS & A Level Maths revision notes

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    Paul

    Author: Paul

    Expertise: Maths

    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 – one of the many reasons he is excited to be a member of the SME team.