Status: Accepted
Owner: smi...@gmail.com
Labels: Type-Defect Priority-Medium Integration
New issue 2310 by smi...@gmail.com: improper integral and _eval_interval
http://code.google.com/p/sympy/issues/detail?id=2310
The following gives the wrong answer:
h[1] >>> F=1/x/(1-x)
h[1] >>> f=F.diff(x)
h[1] >>> integrate(f,x)
1/x + 1/(1 - x)
h[2] >>> integrate(f,(x,0,1))
-oo
partly because _eval_interval is doing the wrong thing:
h[4] >>> F._eval_interval(x,S(0),S(1))
-oo
It evaluates F *from the right* at 0 and 1. It should at least evaluate it
from within the interval (i.e. from the right at 0 and from the left at 1).
If the direction issue had been implemented, it would have at least
returned NaN and the doit would know to do something else to evaluate the
integral as an improper integral. But I'm not sure what exists at present
to handle such cases.
I think it should also watch out for the case where a bounded limit gives
and unbounded value and use the limit to double check it in that case, e.g.
f(x).subs(x, bounded) -> unbounded should check that the limit of f(x) as x
-> bounded.
One approach to calculating this integral would be to do it symbolically in
terms of a parameter and then find the limit as that parameter approaches
the desired value. But when I try this (with intent of letting d -> 1) it
doesn't work because the function is symmetric in the range of 0 to 1 so
the value is 0:
h[1] >>> integrate(f, (x, 1-d, d))
0
See also issue 1116.
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