Question

Simpson's rule clarification:
approximating using Simpson's rule:
1/3W(X+2E+4O)
Where W is common difference, E is sum of even numbers, O is sum of odd and X is the sum of the end values.
I need help because i have found 2 websites which say it is 4 x even and 2 x odd.
while i have found other websites and my textbook saying 2 x even and 4 x odd.
Does anyone know what the actual formula is?

Answer 1

looks correct.... to me... but it depends on how many applications of the rule you need...
the problem you have is to do with the numbering of the x values

if the set of x values are

\[x_{0}, x_{1}, x_{2}, x_{3}. x_{4} ... x_{n - 1} x_{n}\]

the the rule is f(x0) then 2 even and 4 odd....

is the x values are

\[x_{1}. x_{2}, x_{3}, x_{4}....x_{n -1}, x_{n}, x_{n + 1}\]

then its reversed...

so it depends on how you look at it.

Answer 2

for me... if I have the function I just use repeated applications of

\[\int\limits_{a}^{b} f(x) dx = \frac{b - a}{6}[f(a)+ 4f(\frac{a + b}{2}) + f(b)]\]

just keeps things simple... used 3 values.... so find an area, find the next.. etc... and then add the areas.

Answer 3

I do not have the function i am finding the cross sectional are of a river at various tide times.
The depth changes with time.
This means that before the tide comes in i have a smaller area than high tide.
Can you please expand on what you were saying about the numbering of the x values. My x values are depths which range from 0cm to about 300cm.

Answer 4

ok... so here is one way of numbering