Numerical Integration using the Trapezoidal Rule (DP IB Applications & Interpretation (AI)): Revision Note

Trapezoid Rule: Numerical Integration

What is the trapezoid rule?

• The trapezoidal rule is a numerical method used to find the approximate area enclosed by a curve, the-axis and two vertical lines

  • it is also known as ‘trapezoid rule’ and ‘trapezium rule’

• The trapezoidal rule finds an approximation of the area by summing up the areas of trapezoids that lie (mostly) beneath the curve
  

  • For , with , etc., the approximation is given by

where 

• Note that there are  trapezoids (also called strips), but  function values 

What else can I be asked to do with the trapezoid rule?

• Comparing the true answer with the answer from the trapezoid rule

  • This may involve finding the percentage error in the approximation

  • The true answer may be given in the question, found from a GDC or from work on integration