|Re: Impressive TI NSpire CX CAS Multiple Integration|
Message #40 Posted by Valentin Albillo on 21 Dec 2011, 4:37 p.m.,
in response to message #37 by Gerson W. Barbosa
It will understand the following syntax:
integrate tan(x*y*z*t*a*b) dx dy dz dt da db, x=0..1, y=0..1, z=0..1, t=0..1, a=0..1, b=0..1
Trying that syntax out in W/A with the 2-dimensional version, namely:
integrate tan(x*y) dx dy, x=0..1, y=0..1
produces 0.275687 after a while and refuses to compute any more digits ("Computation timed out") which is pretty useless for identification purposes.
On the other hand, the HP-71B produces with the help of just a little code (and my constant recognition program):
workfile BASIC 54 07/18/04 12:38
10 DEF FNF(X)=INTEGRAL(0,1,0,TAN(X*IVAR))
20 DISP INTEGRAL(0,1,0,FNF(IVAR))
> CALL @ CALL IDENTIFY(RES,S$) @ S$
.2756872738 ("identified as") 5/179*Pi^2
which seems quite a reasonable agreement as the alleged symbolic identification evaluates to .275687273774, i.e., a 10-digit agreement with the numerically computed value for the double integral.
Whether the symbolic identification is absolutely correct would require many more digits and that would only serve as empirical reassuring, never proof, that would demand symbolics.
Oh, and by the way, a Monte-Carlo run with 107samples produces .275716754735, which is good to nearly 5 digits, not bad for a dumb probabilistic method.
Best regards from V.
Edited: 21 Dec 2011, 4:50 p.m.