Trapezium Rule (Numerical Integration) (Edexcel IAL Maths)

Spec point — 8.3

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

$\int_{a}^{b} y d x≈1 \frac{1}{2} h \{ ( y_{0}+y_{n} )+2 ( y_{1}+y_{2}+...+y_ n−1 end_ ) \}$ where $h=\frac{b-a}{n}$

• If you have n strips then you need n + 1 y-values

How do I know if it is an underestimate or an 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

Exam Hint The formula for the trapezium rule is given in the formula booklet.

Worked Example