Services & Resources / Wolfram Forums
MathGroup Archive
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2003

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Integrate 5.0

  • To: mathgroup at
  • Subject: [mg44244] Re: Integrate 5.0
  • From: CliffMitchel142 at (Cliff Mitchel)
  • Date: Fri, 31 Oct 2003 03:01:09 -0500 (EST)
  • References: <bnnvfj$61s$>
  • Sender: owner-wri-mathgroup at

You can have the behaviour that you ask for by using the option

Eg start your session with

But I am not sure, even with your expectation that you are working
with real numbers only, that you really want this.

If you force an unconditional answer for your example, the result is
wrong for x>Pi, or x<-Pi

Instead try
Assuming[x \[Element] Reals, Integrate[Sqrt[Cos[t] + 1], {t, 0, x}]]

Or start your session with
$Assumptions=x \[Element] Reals;

Selwyn Hollis <sh2.7183 at> wrote in message news:<bnnvfj$61s$1 at>...
> 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

  • Prev by Date: Re: Integrate 5.0
  • Next by Date: Re: Integrate 5.0
  • Previous by thread: Re: Integrate 5.0
  • Next by thread: Re: Integrate 5.0