Area Between 2 Curves (Edexcel IAL Maths)

Spec point — 8.2

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 Hint

• 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