Harder Substitution (CIE A Level Maths: Pure 3)

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Harder Substitution

What is integration by substitution?

  • Make sure you are familiar with Reverse Chain Rule and Substitution (RCR)
  • In more difficult questions the substitution will be given to you

Notes subst_giv_eg, AS & A Level Maths revision notes

How do I integrate using a given substitution?

  • The process is very much the same as before but expect the algebra to be trickier

Notes subst_giv_eg_soln1, AS & A Level Maths revision notes Notes subst_giv_eg_soln2, A Level & AS Level Pure Maths Revision Notes

  • STEP 1: Differentiate the substitution and rearrange
    • fraction numerator d u over denominator d x end fraction here can be treated like a fraction (eg × dx to get rid of fractions)
  • STEP 2: Replace all parts of the integral
    • all x terms should be replaced with equivalent u terms, including dx
    • if a definite integral change the limits from x to u too
  • STEP 3: Integrate and either
    • substitute x back in or
    • evaluate the definite integral using the u limits
  • STEP 4: Find c, the constant of integration, if needed

Worked example

Example soltn1, A Level & AS Level Pure Maths Revision NotesExample soltn2, A Level & AS Level Pure Maths Revision NotesExample soltn3, A Level & AS Level Pure 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.