(35S) Quick integration

[Albert Chan]

With only 3 sample points, I would use Gaussian quadrature.
It is more accurate (exact for quintic polynomial or less), and does not touch end-points.

Code is slightly more complicated, but I think it is worth it.

Code:

def gauss3(f,a,b, w=0.6**0.5):
    c, d = (b+a)/2, (b-a)/2
    g = d*w
    return (f(c-g) + f(c+g) + 1.6*f(c))/1.8 * d

Your example, ∫(√(1+4*x^2), x = 0..1) ≈ 1.47894285754

Simpson  3-pts: 1.48215537045, relative error ≈ -0.217%
Gaussian 3-pts: 1.47910755366, relative error ≈ -0.011%

Update: integral formula corrected.