Question

which of the following expression is known as general Simpson's 1/3rd rule
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Answer 1

Simpson’s 1/3 rule is basically a method to calculate the value of any definite integral, approximately. It determines the value of the integral by calculating under the curve by dividing the area into equal parts.

The formula below represents the Simpson’s 1/3 rule method to calculate the value of integral  $\int\limits^a_b {f(x)} \,dx$

$\int\limits^a_b {f(x)} \,dx$ = $\frac{h}{3}$ [(y0 + yn) + 4(y1 + y3 + ... + yn-1) + 2(y2 + y4 + ... + yn-2)]

where h = $\frac{(b-a)}{n}$

Answer 2

Answer:

For anyone who have confusion about when to use 1/3 and 3/8 rule.

Step-by-step explanation:

First of all, 1/3 rule is applicable only when n is even which means the number of ordinates given is odd while 3/8 rule is applicable if the number of ordinates starting 4 and even but if and only if second condition is applied, where number of ordinates (even) minus 1 is divisible by 3.

Example for number of ordinates:

a.) 3,5,7,9,11.... are numbers of ordinates for first rule..

b.) 4 for second rule, 6 is even but 6-1=5, where 5 is not divisible by 3; 8 is even but 8-1=7 where it is not divisible by 3; 10 is even, 10-1=9 and so we can apply the second rule hence 9 is divisible by 3. In general, to apply second rule we must have these following number of ordinates 4,10, 16, 22, 28, 34 and so on.

c.) In case the number of ordinates is even but subtracted by 1 is not divisible by 3 like 6,8,12 and so on, you can divide the number of ordinates into two parts for example 12, you can separate it 3 and 9, where this two numbers of ordinates are odd and so you can apply the first rule.

d.) Trapezoidal rule has no condition, all number of ordinates can be applied.

- NESTOR DUAN JR.