Formula(s) for composite/multiple-segment trapezoidal rule

[s3a]

Homework Statement

Hello, everyone. :)

I'm looking at several different sources for the composite/multiple-segment trapezoidal rule (for approximating the value of an integral), but the formulas don't seem to agree.

Homework Equations

One place says I ≈ Δx/2 [f(a) + f(b)] + Δx Σ_(i=2)^(N-1) f(x_i).

Another place says I ≈ Δx/2 [f(a) + f(b)] + Δx Σ_(i=2)^(N) f(x_i).

Yet another place says I ≈ Δx/2 [f(a) + f(b) + 2 Σ_(i=1)^(N-1) f(a + iΔx)].

The Attempt at a Solution

Only the first one seems correct to me. Basically, the second one seems to me like it should end at N-1, not N, and the third one seems to me like it should end at N-2, not N-1.

Am I right?

 

[scottdave]

You could set up a simple example, like if you are splitting your integral into 3 trapezoids. Then see how each of these formulas plays out in figuring it.