AQA A Level Maths: Pure复习笔记8.2.10 Area between 2 curves

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


  • 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


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

How do I find the area between two curves?


  •  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

Exam 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