Question

about Simpson's rule for appr. area under the curve.

Answer 1

First, I just want to verify something for any function f(x) in general, with any number of triangles n, and over any interval [a,b] provided that function is defined over this interval.

\[{\bf\normalsize Sim p.~Rul e.~}= \\ \small~\frac{\Delta x}{3}\left( ~ f(x_0)+4f(x_1)+2f(x_2) +4f(x_3)+2f(x_4)+{\bf ...}+4f(x_{n-1})+2f(x_n) \right)\]\[{\rm where},~~\Delta x~~{\rm is},~~~\frac{b-a}{n}\]

So, why does n have to be an even number?

Answer 2

so b-a can go in it evenly

Answer 3

can you elaborate on this a little?

Answer 4

Maybe I can make some sense from it.