AQA A Level Maths: Pure复习笔记10.1.5 Trapezium Rule (Numerical Integration)

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
10.1.5-Numerical-Integration-Diagram-1

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

10.1.5-Numerical-Integration-Diagram-2a

10.1.5-Numerical-Integration-Diagram-2b

Exam Tip

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

Worked Example

10.1.5-Numerical-Integration-Example-Solution

 

 

 

 

 

 

转载自savemyexams

更多Alevel课程
翰林国际教育资讯二维码