On Apr 10, 2009, at 11:19 AM, davidp wrote:
>
> The following seems like odd behavior to me.
>
> Dave
>
> I. No problem:
> sage: integral(log(x)/x^(1.002),x)
> 500*(-log(x)/x^(1/500) - 500/x^(1/500))
> sage: s(10)-s(1)
> 500*(-log(10)/10^(1/500) - 500/10^(1/500)) + 250000
> sage: n(_)
> 2.64282437870861
>
> II. Problem:
> sage: integral(log(x)/x^(1.002),x,1,10)
...
> III. Problem:
> sage: numerical_integral(log(x)/x^(1.002),x,1,10)
It doesn't take the variable of integration (as there can be only one
unbound variable). The fact that it doesn't is probably a bug, for
consistency the notation
numerical_integral(f, (x, a, b))
should be accepted. See the docstring:
sage: numerical_integral?
Type: builtin_function_or_method
Base Class: <type 'builtin_function_or_method'>
String Form: <built-in function numerical_integral>
Namespace: Interactive
Docstring:
Returns the numerical integral of the function on the interval
from a to b and an error bound.
EXAMPLES:
To integrate the function x^2 from 0 to 1, we do
sage: numerical_integral(x^2, 0, 1, max_points=100)
(0.33333333333333331, 3.7007434154171879e-15)
sage: numerical_integral(log(x)/x^(1.002),1,10)
(2.6428243786881045, 2.9341244752602076e-14)
- Robert
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