# 1 Press Ctrl-A ©G Dear2009 – Not to be sold/Free to use Simpson’s Rule Stage 6 - Year 12 General Mathematic (HSC)

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1 Press Ctrl-A ©G Dear2009 – Not to be sold/Free to use Simpson’s Rule Stage 6 - Year 12 General Mathematic (HSC)

2 A method of approximating irregular areas. Area = (d f + 4 d m + d L ) FirstMiddleLast x x2x2 x2x2 h3h3 Simpson ’ s Rule End of Slide dfdfdfdf dmdmdmdm dLdLdLdL

3 Thomas Simpson ’ s Rule Thomas Simpson (August 20, 1710 – May 14, 1761) was born in Market Bosworth, Leicestershire. The son of a weaver, Simpson taught himself mathematics. He taught mathematics at the Royal Military Academy, Woolwich. Bonaventura Cavalieri Apparently, the method that became known as Simpson's rule was well known and used earlier by Bonaventura Cavalieri (a student of Galileo) in 1639, later rediscovered by James Gregory, and was only attributed to Simpson. End of Slide

4 22m24m20m 60m 30m A = (d f + 4 d m + d l ) h3h3 = (22 + 4 x 24 + 20) 30 3 = 1 380 m 2 Simpson ’ s Rule End of Slide

5 22m24m20m 30m A = (d f1 + 4 d m1 + d l1 ) h3h3 = (22 + 4 x 26 + 24) 15 3 = 1 470 m 2 For a better result, use Simpson ’ s rule twice. 26m 25m 15m + (d f2 + 4 d m2 + d l2 ) h3h3 + (24 + 4 x 25 + 20) 15 3 60m Simpson ’ s Rule End of Slide

6 Simpson ’ s Rule A = (d f1 + 4 d m1 + d l1 ) h3h3 = (0 + 4 x 5 + 2) 12 3 = 200 m 2 Simpson ’ s rule can be used twice here. + (d f2 + 4 d m2 + d l2 ) h3h3 + (0 + 4 x 7 + 0) 12 3 0m5m 0m7m0m 12m 24m 2m End of Show

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