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
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
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
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