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

1. Jul 22, 2017

s3a

1. The problem statement, all variables and given/known data
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.

2. Relevant 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)].

3. 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?

2. Jul 22, 2017

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.