Trapezium Rule (Numerical Integration) (Cambridge International AS Mathematics)

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

integral _ a ^ b y d x ~= 1 half h left curly bracket ( y _ 0 + y _ n ) + 2 ( y _ 1 + y _ 2 +... + y _ n - 1 end _ ) right curly bracket 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

Exam Hint The formula for the trapezium rule is not given in the formula booklet. You must remember it.

Worked Example