Area between a curve and a line (Edexcel A Level Maths) : Revision Note

Did this video help you?

Area between a curve and a line

What is the area between a curve and a straight line?

Notes fig1, AS & A Level Maths revision notes
  • This is the area enclosed by a curve and a line between their intersections

  • The intersections may need to be found using simultaneous equations

How do I find the area between a curve and a line?

  • The area enclosed will be the difference between …

    • the area under the curve and

    • the area under the line

  • These can be found separately

 

Notes fig2, AS & A Level Maths revision notes
  • There may be easier ways to find the area under a line

 

Notes fig3, AS & A Level Maths revision notes
  • Once the areas are found a question can be answered in full

Notes fig4, AS & A Level Maths revision notes

 

Notes fig5, AS & A Level Maths revision notes

 

Notes fig6, AS & A Level Maths revision notes
  • STEP 1: Find the intersections of the line and the curve

  • STEP 2: Find the area under a curve, RC, using definite integration

  • STEP 3: Find the area under a line, RL, either using definite integration or the area formulae for basic shapes

  • STEP 4: To find the area, R, between the curve and the line subtract the smaller area from the larger area

    • If curve on top this will be RC – RL

    • If line on top this will be RL - RC

Alternative method

  • An alternative method allows subtraction of the two functions first

  • But be extremely careful as to whether the curve or the line is on top

 

Notes fig7, AS & A Level Maths revision notes
  • STEP 1: Find the intersections of the line and the curve

  • STEP 2: Subtract the functions algebraically

    • Ensure this is done the correct way round!

  • STEP 3: Find the area, R, between the curve and the line using definite integration

Notes fig8, A Level & AS Level Pure Maths Revision Notes
Notes fig9, AS & A Level Maths revision notes

Examiner Tips and Tricks

  • Add information to any diagram provided

  • Add axes intercepts, as well as intercepts between lines and curves

  • Mark and shade the area you’re trying to find

  • If no diagram provided, sketch one!

Worked Example

Example Question fig1, A Level & AS Level Pure Maths Revision Notes
Example fig2, A Level & AS Level Pure Maths Revision Notes
Example fig3, AS & A Level Maths revision notes
Example fig4, AS & A Level Maths revision notes
👀 You've read 1 of your 5 free revision notes this week
An illustration of students holding their exam resultsUnlock more revision notes. It's free!

By signing up you agree to our Terms and Privacy Policy.

Already have an account? Log in

Did this page help you?

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.

Download notes on Area between a curve and a line