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Trapezium Rule (Numerical Integration) (OCR A Level Maths: Pure)
Revision Note
Trapezium Rule (Numerical Integration)
What is the trapezium rule?
- The trapezium rule is a numerical method of integration used to find the approximate area under a curve
- It can be used when analytical methods of integration won’t work
- It finds an approximation of the area by finding the sum of the areas of trapeziums beneath the curve
- The formula for an estimate of the area when splitting it into n strips (trapezium) is
where
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- If you have n strips then you need n + 1 y-values
Underestimate or overestimate?
- Depending on the shape of the curve, the trapezium rule could be an underestimate or overestimate
- The more trapezium strips used the more accurate the estimate
- Calculating the percentage error can tell you how accurate your estimate is
- Using rectangular strips can find the upper and lower bounds of the interval for the trapezium rule
Examiner Tip
The formula for the trapezium rule is given in the formula booklet.
Worked example
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