Difference between revisions of "Simpson's rule"
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==Other Versions of Simpson's Rule== | ==Other Versions of Simpson's Rule== | ||
There are a few other rules that Simpson proved. For example, Simpson's 3/8 Rule<ref>http://math.fullerton.edu/mathews/n2003/Simpson38RuleMod.html</ref> shows that cubic functions can be used to approximate integrals. | There are a few other rules that Simpson proved. For example, Simpson's 3/8 Rule<ref>http://math.fullerton.edu/mathews/n2003/Simpson38RuleMod.html</ref> shows that cubic functions can be used to approximate integrals. | ||
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| + | ==See also== | ||
| + | *[[Calculus]] | ||
| + | *[[Integration]] | ||
| + | *[[Methods of integration]] | ||
| + | *[[Riemann Integral]] | ||
== References == | == References == | ||
Revision as of 19:10, December 30, 2008
In Calculus, Simpson's Rule is a method of approximating integrals by using parabolas or other higher order polynomial expressions. It is named after its discoverer, Thomas Simpson[1].
Contents
Simpson's Rule
Specifically, Simpson's Rule states:
Composite Simpson's Rule
Simpson's Rule can be applied to segments of an integral, effectively making it a Riemann Integral.
If the interval 
is split into 
segments, with as an even number, there is a formula that can be used to solve for the integral.
Note that:
As an extension of Simpson's Rule, we can find that:
The above formula can be rewritten as:
- The formulas above do not work unless is even.
Other Versions of Simpson's Rule
There are a few other rules that Simpson proved. For example, Simpson's 3/8 Rule[2] shows that cubic functions can be used to approximate integrals.
