Numerical integration vs. integrals that are zero

[Albert Chan]

(03-06-2019 02:19 PM)Thomas Klemm Wrote:  Cf. About the Algorithm

Noticed a typo, transformed integral involve 2 substitutions, not 1:

x = (b-a)/2 * v + (b+a)/2, to transform integration range from [a,b]  to [-1,1]
v = 3u/2 - u³/2, nonlinear transformed, integration range from [-1,1] to (-1, 1)

PHP Code:

def nonlinear(f, a, b):
    c, d = (b-a)/4, (b+a)/2
    def t(u, k=3.*c):
        eps = 1.0 - u*u      # return 0 if eps=0
        return eps and k*eps * f(c*u*(eps + 2.) + d)
    return t 


With nonlinear defined, integrate(f, a, b) = integrate(nonlinear(f, a, b), -1, 1)