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Re: Re: Integrate 5.0
*To*: mathgroup at smc.vnet.net
*Subject*: [mg44264] Re: [mg44237] Re: Integrate 5.0
*From*: Selwyn Hollis <sh2.7183 at misspelled.erthlink.net>
*Date*: Tue, 4 Nov 2003 03:23:35 -0500 (EST)
*References*: <bnnvfj$61s$1@smc.vnet.net> <200310310801.DAA09815@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Thanks to all for pointing out the GenerateConditions option. I must
plead guilty to the unoriginal sin of not consulting the documentation.
It is somewhat awkward to use options in Integrate though, since it
forces you either to use the input form of Integrate or to use
SetOptions. But I'm nitpicking...
-----
Selwyn Hollis
http://www.math.armstrong.edu/faculty/hollis
On Oct 31, 2003, at 3:01 AM, Jens-Peer Kuska wrote:
> 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
>
>
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