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[Mathematica 6] Integrate strange result
*To*: mathgroup at smc.vnet.net
*Subject*: [mg78325] [Mathematica 6] Integrate strange result
*From*: Nasser Abbasi <nma at 12000.org>
*Date*: Thu, 28 Jun 2007 04:29:22 -0400 (EDT)
In[13]:= $Version
Out[13]= 6.0 for Microsoft Windows (32-bit) (April 27, 2007)
The problem is this: When I ask Mathematica to integrate something
involving some constant parameter, it gives an answer for some range
of the constant involved, say range A, and it says there is no answer
for the other range, say range B
But next, when I specify, using assumptions, that the constant is now
in range B, then Mathematica does given an answer to the integral !
Why does it in one case say there is no answer if the constant is in
range B, and in the second case it gives an answer when the constant
is in range B?
case 1
========
In[2]:= f = (1 + k*Sin[a]^2)^(1/2);
In[12]:= Assuming[Element[k, Reals], Integrate[f, {a, 0, 2*Pi}]]
Out[12]= If[k >= -1, 4*EllipticE[-k], Integrate[Sqrt[1 +
k*Sin[a]^2], {a, 0, 2*Pi}, Assumptions -> k < -1]]
notice in the above, it says for k<-1 there is NO answer
case 2
=======
In[2]:= f = (1 + k*Sin[a]^2)^(1/2);
In[10]:= Assuming[Element[k, Reals] && k < -1, Integrate[f, {a, 0,
2*Pi}]]
Out[10]= 0
Notice in the above, for k<-1 it gives an answer, which is zero.
What is it I am missing here?
thanks
Nasser
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