Could you try specific "n" cases (4 and 6)
sage: integrate((cos(t)^n+sin(t)^n)^(1/2), t,0,pi)
and
sage: integrate((cos(t)^6+sin(t)^6)^(1/2), t,0,pi)
Thanks,
Alex
On Sep 7, 12:28 pm, William Stein <wst...@gmail.com> wrote:
> On Mon, Sep 7, 2009 at 9:19 AM, Alexander
>
>
>
> R.Povolotsky<apovo...@gmail.com> wrote:
>
> > For
> > Int((cos(t)^n+sin(t)^n)^(1/2),t = 0 ... Pi)
> > that is
> > Integrate[Sqrt[Cos[t]^n + Sin[t]^n], {t, 0, Pi}]
>
> > 1) n=4
> > Maple gives
> > EllipticE(I)*sqrt(2)
> > vs
> > Mathemtica's
> > 2*EllipticE[1/2]
>
> > and
> > 2) n=6
> > Maple gives
> > EllipticE(sqrt(3)*I)
> > vs
> > Mathematica's
> > 2 EllipticE[3/4]
>
> > In both cases above Maple has explicit reference to the imaginary
> > part I and Mathematica doesn't ...
>
> > What Sage does on that ?
>
> Here's what Sage (=Maxima in this case) does:
>
> sage: var('t,n')
> (t, n)
> sage: integrate((cos(t)^n+sin(t)^n)^(1/2), t,0,pi)
> integrate(sqrt(sin(t)^n + cos(t)^n), t, 0, pi)
>
> i.e., nothing, it doesn't know how to compute that integral.
>
> -- William
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