Trapezium Rule (Numerical Integration) (Cambridge (CIE) AS Maths) : 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

• 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