Trapezium Rule (Numerical Integration) (OCR A Level Maths: Pure)

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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 strips (trapezium) is
integral subscript a superscript b y d x almost equal to 1 half h left curly bracket left parenthesis y subscript 0 plus y subscript n right parenthesis plus 2 left parenthesis y subscript 1 plus y subscript 2 plus... plus y subscript n minus 1 end subscript right parenthesis right curly bracket where h equals fraction numerator b minus a over denominator n end fraction
    • If you have strips then you need + 1 y-values

Numerical Integration Diagram 1, AS & A Level Maths revision notes

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

 

Numerical Integration Diagram 2a, AS & A Level Maths revision notes

Numerical Integration Diagram 2b, AS & A Level Maths revision notes

Examiner Tip

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

Worked example

Numerical Integration Example Solution, AS & A Level Maths revision notes

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Lucy

Author: Lucy

Expertise: Head of STEM

Lucy has been a passionate Maths teacher for over 12 years, teaching maths across the UK and abroad helping to engage, interest and develop confidence in the subject at all levels. Working as a Head of Department and then Director of Maths, Lucy has advised schools and academy trusts in both Scotland and the East Midlands, where her role was to support and coach teachers to improve Maths teaching for all. Lucy has created revision content for a variety of domestic and international Exam Boards including Edexcel, AQA, OCR, CIE and IB.