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MathGroup Archive 2003

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Re: Integrate 5.0

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44244] Re: Integrate 5.0
  • From: CliffMitchel142 at hotmail.com (Cliff Mitchel)
  • Date: Fri, 31 Oct 2003 03:01:09 -0500 (EST)
  • References: <bnnvfj$61s$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

You can have the behaviour that you ask for by using the option
GenerateConditions->False

Eg start your session with
SetOptions[Integrate,GenerateConditions->False]

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 misspelled.erthlink.net> wrote in message news:<bnnvfj$61s$1 at smc.vnet.net>...
> 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


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