## How to Approximate Area with Simpson's Rule - dummies

In mathematics, the most widely used solutions for the described class of numerical integration problems include the Trapezoidal Rule, Gauss Quadrature, and Simpson’s Rule. Gauss Quadrature is probably the most accurate method, but for most engineering solutions, I have found that the Simpson’s Rule is a reliable method and the easiest to use. 1. Mar 05, · Best Answer: One application of simpson's rule is: (h/3)(1st + 4 * 2nd + 3rd) If you were to apply it twice, on a function sampled 5 times, then it would be: (h/3)(1st + 4 * 2nd + 3rd) + (h/3)(3rd + 4 * 4th + 5th) = (h/3)(1st + 4 * 2nd + 2 * 3rd + 4 * 4th + 5th) In general, the formula goes: (h/3)(1st + 4 Status: Open. Proof of Simpson's Rule. We consider the area under the general parabola `y=ax^2+bc+c`. For easier algebra, we start at the point `(0,y_1)`, and consider the area under the parabola between `x=-h` and `x=h`, as shown. (Note that `Delta x = h`.) We have: `int_(-h)^h (ax^2+bx+c)\ dx ` .

## 6. Simpson's Rule

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For this one for example there are four numbers but if you graphed this from 0. Report Abuse. Are you sure that you want to delete this answer? Yes No. Try it again with this new formula. Source s :. Add a comment. Asker's rating. Existing questions. Related Questions I need help applying Simpson's rule?

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### How do you apply the Simpson's rule twice? | Yahoo Answers

Proof of Simpson's Rule. We consider the area under the general parabola `y=ax^2+bc+c`. For easier algebra, we start at the point `(0,y_1)`, and consider the area under the parabola between `x=-h` and `x=h`, as shown. (Note that `Delta x = h`.) We have: `int_(-h)^h (ax^2+bx+c)\ dx ` . In general, Simpson’s rule gives a much better estimate than either the midpoint rule or the trapezoid rule. A Simpson’s rule sum or approximation is sort of an average of a midpoint sum and a trapezoid sum, except that you use the midpoint sum twice in the average. In mathematics, the most widely used solutions for the described class of numerical integration problems include the Trapezoidal Rule, Gauss Quadrature, and Simpson’s Rule. Gauss Quadrature is probably the most accurate method, but for most engineering solutions, I have found that the Simpson’s Rule is a reliable method and the easiest to use. 1.