Problem with integral on WP 34s
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09-12-2021, 11:15 PM
(This post was last modified: 09-13-2021 09:39 AM by Albert Chan.)
Post: #23
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RE: Problem with integral on WP 34s
(09-12-2021 08:41 PM)Nigel (UK) Wrote: The comments from [double exponential] integration code state that 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') |
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