On Wed, Mar 11, 2009 at 2:52 PM, mark mcclure <mcmcc...@unca.edu> wrote:
>
>
>
> On Mar 11, 2:46 pm, David Joyner <wdjoy...@gmail.com> wrote:
>> sage: t = var("t")
>> sage: numerical_integral(abs(sin(t^2)),0,3)
>> (1.7024100330599248, 1.5397333279914378e-06)
>>
>> because AFAIK, integrate(abs(sin(t*t)),t,0,3)
>> cannot be computed in closed form.
>
> Mathematica returns the result in terms of Fresnel functions.Point taken. However, integrate(abs(sin(t*t)),t,0,3) is by definition (since sin(x)>0 in that interval) the Fresnel integral S(3), http://en.wikipedia.org/wiki/Fresnel_integral, and just renaming it doesn't make it a closed form expression:-) > Maxima can find the indefinite integral in terms of the error > function. What Maxima *can't* do is deal with absolute values > in a definite integral. Try: > integrate(abs(sin(t)), t, 0, pi) > > The result returns unevaluated, even though the integrand is > positive on the integral. I think I saw that on the Maxima > discussion group a bit ago. > > Mark McClure > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
