Thomas Simpson published Simpson's Rule in 1743, which uses parabolas instead of straight lines to better approximate the area under a curve. Simpson's Rule requires an even number of intervals or ordinates and is more accurate than the Trapezium Rule. Two examples are provided where Simpson's Rule is used with either five ordinates or four intervals to estimate the value of integrals.

1. Starter Use the Trapezium Rule with four intervals to estimate the value of Have you overestimated or underestimated the true area? 3.28 (3 s.f.)

2. Objective: to understand Simpson’s Rule Thomas Simpson (1710 – 1761)

3. Simpson’s Rule Simpson’s Rule was actually invented by Sir Isaac Newton but Thomas Simpson published it again in 1743. It is more accurate than the Trapezium Rule because it fits a number of parabolas to the curve rather than straight lines. To use Simpson’s Rule, you must have an even number of intervals (or an odd number of ordinates).

4. Example 1 Use Simpson’s Rule with five ordinates to find the approximate value of 3.24 (3 s.f.)

5. Example 2 Use Simpson’s Rule with four intervals to find the approximate value of 2.87 (3 s.f.)

6. Core 3 & 4 Textbook Exercise 12B Page 188