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Topic: should CAS resturn infinity for divergent integral or a message that
integral diverges?

Replies: 9   Last Post: Apr 19, 2014 1:49 AM

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Nasser Abbasi

Posts: 5,674
Registered: 2/7/05
should CAS resturn infinity for divergent integral or a message that
integral diverges?

Posted: Mar 11, 2014 9:04 PM
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May be this is an API design preference, or may be
there can be a deep mathematical to prefer one over
the other.

Which you think is the better response in the case
when one asks cas to integrate something that does not
converge over the limit of integration? return infinity,
or issue an error message?

What does your CAS return?

----------------------
Maple, return infinity:

int(1/sqrt(x),x=0..infinity);
(* infinity *)
----------------------

Mathematica: issues a red message with a beep and
return the original integral unevaluated:

Integrate[1/Sqrt[x], {x, 0, Infinity}]
Integrate::idiv: Integral of 1/Sqrt[x] does
not converge on {0,\[Infinity]}. >>
Integrate[1/Sqrt[x], {x, 0, Infinity}]

---------------------
Matlab mupad, same as Maple:

int( 1/sqrt(x),x,0,inf)
ans =

Inf

----------------------
maxima 12.04: Similar to Mathematica. Gives an error:

integrate(1/sqrt(x),x,0,inf);
defint: integral is divergent.
an error. To debug this try: debugmode(true);

----------------------


--Nasser



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