I'm not sure if what you report is a bug in SAGE. SAGE calls Maxima. If Maxima
refuses to integrate that integral (and I think it *should* but maybe
the algebra
is too complicated for it) then SAGE won't do it either.
If you want a numerical value then use n(integrate...). That seems to be
"working" though, as in my last email, providing an incorrect answer.
I just entered it as
http://trac.sagemath.org/sage_trac/ticket/3520
Can you check if Maxima (or sympy) can do the integral? If yes to
either, that would be
very interesting.
On Fri, Jun 27, 2008 at 8:08 AM, Roger <[EMAIL PROTECTED]> wrote:
>
> Do I need to do something further to make sure that this gets entered
> as a bug, or do the developers read this list regularly? Thanks.
>
> On Jun 22, 8:23 am, Roger <[EMAIL PROTECTED]> wrote:
>> Huh.
>>
>> Whomever looks at this issue should note that there are now two
>> distinct problems raised in this thread: the original issue regarding
>> why f.integral(9,16) below remains unevaluated, and tDavid's question
>> of why the two answers are different.
>>
>> On Jun 21, 9:01 am, "David Joyner" <[EMAIL PROTECTED]> wrote:
>>
>> > Unless 24.9... = -24.9..., there seems to be a bug:
>>
>> > sage: f = sqrt(25-x)*sqrt(1+1/(4*(25-x)))
>> > sage: f.integral(x,9,16)
>> > integrate(sqrt(1/(4*(25 - x)) + 1)*sqrt(25 - x), x, 9, 16)
>> > sage: f.nintegral(x,9,16)
>> > (24.9153783348643, 2.7661626694613149e-13, 21, 0)
>> > sage: g = f.simplify_radical()
>> > sage: g.integral(x,9,16)
>> > I*(65*sqrt(65)*I/6 - 37*sqrt(37)*I/6)/2
>> > sage: ans = g.integral(x,9,16)
>> > sage: ans.real()
>> > (37*sqrt(37)/6 - 65*sqrt(65)/6)/2
>> > sage: RR(ans.real())
>> > -24.9153783348643
>>
>> > On Sat, Jun 21, 2008 at 8:51 AM, Roger <[EMAIL PROTECTED]> wrote:
>>
>> > > Can someone explain why sage (or perhaps maxima, I don't know) manages
>> > > to evaluate the indefinite integral below, but fails to give a numeric
>> > > answer to the definite integral? Seems odd to me. (version 3.02
>> > > running on Mac OS X)
>>
>> > > sage: var('x')
>> > > x
>> > > sage: integral(sqrt(25-x)*sqrt(1+1/(4*(25-x))),x)
>> > > sqrt(4*x - 101)*(4*I*x - 101*I)/12
>> > > sage: integral(sqrt(25-x)*sqrt(1+1/(4*(25-x))),x,9,16)
>> > > integrate(sqrt(1/(4*(25 - x)) + 1)*sqrt(25 - x), x, 9, 16)
>>
>> > > Thanks,
>> > > Roger
> >
>
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