HP 15C and INT(1/√(1-x),0,1)

[Valentin Albillo]

(01-10-2018 01:33 PM)emece67 Wrote:  Tested on a wp34s (with the last version of the integration routine):

• SCI2: 1.999279690943348 (2 s)
• SCI4: 1.999609653263110 (3 s)
• SCI6: 1.999968878589093 (3 s)
• SCI8:1.999998824537611 (3 s)
• SCI10: 1.999999985077354 (3 s)
• ALL0: 1.999999985077354 (4 s)
• DBLON: 1.999999999999999976156369124294215 (16 s)
  

Actually this integral isn't quite as difficul as it seems when using purely numeric (not CAS) methods, it's just a matter of using some numerical quadrature method suited to the task at hand.

Just for instance my very own implementation of one such method for the barebones HP-71B does return 2.000000000000 (i.e.: exactly 2 to twelve digits) in just 4 seconds when run in J-F Garnier's Emu71 (about 15 min. in a real machine) using an accuracy as low as 1e-4.

Also, the fact that CAS can give the exact value almost instantly is completely irrelevant, most integrals cannot be managed by CAS and even slight changes to this one woul be intractable

V.
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