Area between 2 curves (Edexcel A Level Maths) : Revision Note

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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 Tips and Tricks

  • 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 notes
Example soltn, A Level & AS Level Pure 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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