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ASMaths: Pure 1CIERevision Notes6. Integration6.2 Further Integration6.2.3 Area between 2 curves

Area between 2 curves (CIE AS Maths: Pure 1)

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Area between 2 curves

What is the area between two curves?

  • Ensure you are familiar with …
    • Area under a curve
    • Area between a line and a curve

    Notes curv_easy, AS & A Level Maths revision notes

  • In general find the definite integral of “upper curve” – “lower curve”
  • However this does depend on …
    • … the area being found
    • … if the curves intersect (and cross over)

  • The area may have to be split into separate integrals

 Notes curv_hard, AS & A Level Maths revision notes 

  • The points at which curves intersect may need to be calculated

How do I find the area between two curves?

Notes area_eg, AS & A Level Maths revision notes

  •  STEP 1: Find the intersections of the curves if needed
  • STEP 2: Form the integral …
    • … using the intersections as limits
    • … “upper curve” – “lower curve” …
    • … and find the value of the integral
  • STEP 3: Repeat STEP 2 if more than one area needed
  • STEP 4: Add areas together

Examiner Tip

  • If no diagram is provided sketch one, even if the curves are not accurate.
  • Add information to any given diagram as you work through a question.Maximise use of your calculator to save time and maintain accuracy:
    • Solving equations, especially cubic equations
    • Finding definite integrals

Worked example

Example quest, AS & A Level Maths revision notesExample soltn, 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.