How does Weddle's rule work?

[the_beatbox_god]

I have a maths assignment and I have to explain the quarks of Weddle's rule, I can't find any information on the internet so could someone please explain how it works?

. . . . .\(\displaystyle \displaystyle I\, =\, \int_a^b\, f(x)\, dx\, \cong\, \dfrac{3h}{10}\, \bigg[\, f_0\, +\, 5\, f_1\, +\, f_2\, +\, 6\, f_3\, +\, f_4\, +\, 5\, f_5\, +\, f_6\, \bigg]\)

I very much understand how the Simpson's rule works, using parabolas to estimate the area. Is the Weddle's rule the same? Thanks in advance to anyone who can help me.

 

[SAMUELK]

I have a maths assignment and I have to explain the quarks of Weddle's rule, I can't find any information on the internet so could someone please explain how it works?

. . . . .\(\displaystyle \displaystyle I\, =\, \int_a^b\, f(x)\, dx\, \cong\, \dfrac{3h}{10}\, \bigg[\, f_0\, +\, 5\, f_1\, +\, f_2\, +\, 6\, f_3\, +\, f_4\, +\, 5\, f_5\, +\, f_6\, \bigg]\)

I very much understand how the Simpson's rule works, using parabolas to estimate the area. Is the Weddle's rule the same? Thanks in advance to anyone who can help me.

Yes.

OKAY -- you want some details? It is 'just like' Simpson, just a different form of weighted average.

You chop [a,b] into six subintervals (S's uses two, Trapezoidal uses 1, etc) with evaluation points at:

x0 = a, x1 = a+h, ... x6 = a+6h

and

f0 means f(x0), f1 = f(x1), etc.

I think that's it.