MathGroup Archive 2003

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

Search the Archive

Re: Integrate 5.0

In article <bnnvfj$61s$1 at>,
 Selwyn Hollis <sh2.7183 at> 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).

I don't understand why you don't just compute the indefinite integral? 

The definite integration code is attempting to do a much more 
complicated operation. The checking code in 5.0 appears to more 
carefully check the conditions under which the result is true.

Alternatively, why not help the integrator with appropriate assumptions, 

  Integrate[Sqrt[Cos[t] + 1], {t, 0, x}, Assumptions -> {0 < x < Pi}]

for which you get an even nicer closed form solution.

> 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]

But this answer is only partially incorrect. It is only valid for 
-Pi < t < Pi. To see what I mean, with

  de =  {y'[t] == Sqrt[Cos[t] + 1], y[0] == 0};

  Plot[Evaluate[y[t] /. DSolve[de, y, t]], {t, 0, 10}]; 

to the correct result

  Plot[Evaluate[y[t] /. NDSolve[{de, y, {t, 0, 10}]], {t, 0, 10}]; 


Paul Abbott                                   Phone: +61 8 9380 2734
School of Physics, M013                         Fax: +61 8 9380 1014
The University of Western Australia      (CRICOS Provider No 00126G)         
35 Stirling Highway
Crawley WA 6009                      mailto:paul at 

  • Prev by Date: Re: simple equation system -- crashing M5?
  • Next by Date: Trying to use Mathematica as "word processor" for my math homework
  • Previous by thread: Re: Re: Integrate 5.0
  • Next by thread: ComplexExpand