Re: Integrate 5.0
- To: mathgroup at smc.vnet.net
- Subject: [mg44237] Re: Integrate 5.0
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Fri, 31 Oct 2003 03:01:03 -0500 (EST)
- Organization: Universitaet Leipzig
- References: <bnnvfj$61s$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
I would not recommend it but
SetOptions[Integrate,GenerateConditions->False]
is your friend.
Regards
Jens
Selwyn Hollis wrote:
>
> I've come to the conclusion that Integrate has become nearly worthless
> for computing definite integrals with symbolic limits. To cite a simple
> example,
>
> Integrate[Sqrt[Cos[t] + 1], {t, 0, x}]
>
> returns an awful mess inside of an If statement (very mild in this
> case) that no one should have to deal with if they're only concerned
> with real numbers (specifically calculus students and a great many
> applied mathematicians).
>
> On the other hand, DSolve gives the simple, clean answer that Integrate
> used to give:
>
> y[t]/. DSolve[{y'[t] == Sqrt[Cos[t] + 1], y[0] == 0}, y[t], t]
>
> 2*Sqrt[1 + Cos[t]]*Tan[t/2]
>
> Could it be that we need a new function such as this:
>
> RealIntegral[expr_,{x_,a_,b_}]:=
> (y[x]/. First@DSolve[{y'[x] ==expr, y[a] == 0}, y[t], t])/.x->b
>
> that would be associated with \[Integral] ? ... leaving the current
> Integrate to be associated with \[ContourIntegral]??
>
> Or perhaps a simple option for Integrate like RealLimits->True?
>
> -----
> Selwyn Hollis
> http://www.math.armstrong.edu/faculty/hollis