1. ©G Dear2009 – Not to be sold/Free to use
General Mathematic
(HSC)
Further Applications
of Area & Volume
Tree Diagrams
Stage 6 - Year 12
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©G Dear2009 – Not to be sold/Free to use

2. A method of approximating irregular areas.
Simpson’s Rule
A method of approximating irregular areas. h 3
Area = (df + 4 dm + dL)
First
Middle
Last df dm dL x 2 x 2 x
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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.
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.
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4. Simpson’s Rule h A = (df + 4 dm + dl) 3 30 = (22 + 4 x 24 + 20) 3
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5. For a better result, use Simpson’s rule twice.h 3 h 3
A = (df1 + 4 dm1 + dl1)
+ (df2 + 4 dm2 + dl2) 15 3 15 3
= ( x )
+ ( x )
= m2
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6. Simpson’s rule can be used twice here.3 h 3
A = (df1 + 4 dm1 + dl1)
+ (df2 + 4 dm2 + dl2) 12 3 12 3
= (0 + 4 x 5 + 2)
+ (0 + 4 x 7 + 0)
= 200 m2
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