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Re: Re: Simple integral wrong
*To*: mathgroup at smc.vnet.net
*Subject*: [mg25166] Re: [mg25107] Re: Simple integral wrong
*From*: David Withoff <withoff at wolfram.com>
*Date*: Tue, 12 Sep 2000 02:58:52 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
> Hi all,
>
> This leaves even more questions, actually I would prefer the first
> "result"...
>
> Mathematica 4.0 for Linux
> Copyright 1988-1999 Wolfram Research, Inc.
> -- Motif graphics initialized --
>
> In[1]:= Integrate[Abs[Cos[x]],x]
>
> Out[1]= Integrate[Abs[Cos[x]], x]
>
Giving up on the problem is certainly one way to always
return a correct result. In this particular example, giving
up would probably have led to the expected result. Your
choice might have been different, of course, but the designers
of Mathematica decided in this example that giving up was not
in general the most useful thing to do.
> Note that also the Differentiation goes wrong (which might be th reason
> for the wrong Integration after all):
>
> Mathematica 4.0 for Linux
> Copyright 1988-1999 Wolfram Research, Inc.
> -- Motif graphics initialized --
>
> In[1]:= Integrate[Abs[Cos[x]],{x,0,y}]
>
> 2
> Out[1]= Sqrt[Cos[y] ] Tan[y]
>
> In[2]:= Integrate[Abs[Cos[x]],{x,0,y}] // InputForm
>
> Out[2]//InputForm= Sqrt[Cos[y]^2]*Tan[y]
>
> In[3]:= D[Sqrt[Cos[y]^2]*Tan[y],y] // Simplify
>
> 2
> Out[3]= Sqrt[Cos[y] ]
The differentiation is fine if everything is real, which
seems to be an implicit assumption for this calculation anyway.
Dave Withoff
Wolfram Research
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