Re: integrat trig radical
- To: mathgroup at smc.vnet.net
- Subject: [mg39588] Re: [mg39575] integrat trig radical
- From: BobHanlon at aol.com
- Date: Tue, 25 Feb 2003 02:55:20 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
In a message dated 2/24/03 3:38:54 AM, mathefritz at schmieder-laher.de writes:
> is there any mathematical reason for mathematica, not 1st internally
> using
> Cos[x/2] = Sqrt[(1 + Cos[x])/2]
> before
> integrating Sqrt[1 + Cos[x]] ?
> It
> even refuses to answer True
> to
> Integrate[Sqrt[1 + Cos[x]],x] == 2*Sqrt[2]*Sin[x/2]
>
Needs["Graphics`Colors`"];
Plot[{Sqrt[1 + Cos[x]], Sqrt[2]*Cos[x/2]},
{x,-2Pi,2Pi}, PlotStyle->{Red,Blue}];
FullSimplify[Integrate[Sqrt[1 + Cos[x]],x] == 2*Sqrt[2]*Sin[x/2], -Pi<=x<=Pi]
True
Bob Hanlon