Problem with integral on WP 34s

[Albert Chan]

(09-12-2021 08:41 PM)Nigel (UK) Wrote:  The comments from [double exponential] integration code state that

Quote:the double exponential method relies on the function to be
integrated being analytic over the integration interval, except,
perhaps, at the interval ends

Even if integrand is analytic, it may be wise to break-up integral.

Example, ∫(z^(1/3), z = -2 .. 3)

>>> from mpmath import *
>>> def f(x): f.n+=1; return cbrt(x) # complex cube root, principle branch
...
>>> f.n=0; quad(f, (-2,3), error=1), f.n
((mpc(real='4.1920063238379486', imag='1.6347100863481141'), mpf('0.01')), 427)

Now, break-up integral to 2 pieces.

>>> f.n=0; quad(f, (-2,0,3), error=1), f.n
((mpc(real='4.1900023206128241', imag='1.6366854539575821'), mpf('1.0e-24')), 106)

>>> F = lambda z: mpc(z)**(4/3)/(4/3)
>>> F(3) - F(-2) # integral true value
mpc(real='4.1900023206128232', imag='1.6366854539575817')
>>> F(3) + F(2)*exp(pi/3*1j) # another way
mpc(real='4.1900023206128232', imag='1.6366854539575821')