# The Accuracy of Simpson's Rule

• fonseh
In summary, the conversation is about applying Simpson's rule to find an answer for part b of a homework question. The person asks why their answer is different from the author's, and the response explains that both 1/3 and 3/8 Simpson's rule were used, with different intervals, resulting in a 5% deviation. The person is also asked if they understand the basis and appropriateness of using Simpson's rule.
fonseh

## Homework Statement

For part b , Since 3/8 Simpson's rule and 1/3 Simpson's rule can't be applied directly to get the ans , so i have to apply both methods differently .

I
Why my ans is different with the author's one ? Is there anything wrong with my ans ?

## The Attempt at a Solution

n my third attachment , I apply the 1/3 Simpson's rule first ( for interval 0-4) , i get the ans = 3208

Then , I apply 3/8 Simpson's rule ( for interval 0-6) , i get ans = 3597.5 .

Sum of 3208 and 3597.5 = 6805.2 , but , in the author's working , The author apply 3/8 simspon's rule first , followed by 1/3 Simspon's rule , the author get the total ans = 7198.75 ...

#### Attachments

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Hello fonseh,

This exercise is an example of applying Simpson's rule. Do you know what that rule is based on ? Do you think it is always approriate to use when you look at a plot of v versus t ? Is it surprising that the deviation of two different subdivisions gives such a 5% deviation ?

fonseh and Chestermiller

## 1. What is Simpson's rule?

Simpson's rule is a mathematical formula used for numerical integration, or estimating the area under a curve, by dividing the curve into smaller sections and approximating each section with a parabola.

## 2. What is 1/3 Simpson's rule?

1/3 Simpson's rule is a specific case of Simpson's rule where the curve is divided into three sections and each section is approximated with a parabola. It is often used when the number of data points is odd.

## 3. What is 3/8 Simpson's rule?

3/8 Simpson's rule is another specific case of Simpson's rule where the curve is divided into four sections and each section is approximated with a parabola. It is often used when the number of data points is a multiple of three.

## 4. When should I use 1/3 Simpson's rule versus 3/8 Simpson's rule?

1/3 Simpson's rule should be used when the number of data points is odd, while 3/8 Simpson's rule should be used when the number of data points is a multiple of three. If the number of data points is even and not a multiple of three, either rule can be used with similar accuracy.

## 5. How accurate is Simpson's rule compared to other numerical integration methods?

Simpson's rule is generally more accurate than other numerical integration methods, such as the trapezoidal rule or midpoint rule, because it takes into account the curvature of the curve. However, its accuracy can still be affected by the number of data points and the complexity of the curve.

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