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
