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Why this simply elliptic integral fails
*To*: mathgroup at smc.vnet.net
*Subject*: [mg36409] Why this simply elliptic integral fails
*From*: "Raf" <r_a_f at yahoo.it>
*Date*: Wed, 4 Sep 2002 21:22:28 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
Hi,
This result seems to me to be wrong (it's right?):
In[1]:=
Integrate[Sqrt[a^2*Cos[t]^2 + b^2*Sin[t]^2],
{t, 0, 2*Pi}, Assumptions->{Im[a]==0, Im[b]==0}]
Out[1]=
0
....but written in another way, it's right:
In[2]:=
Integrate[Sqrt[a^2 + (b^2 - a^2)*Sin[t]^2],
{t, 0, 2*Pi}, Assumptions ->
{Im[a] == 0, Im[b] == 0}]
Out[2]=
If[a^2/(-a^2 + b^2) >= 0 ||
b^2/(-a^2 + b^2) <= 0 ||
Im[a^2/(-a^2 + b^2)] != 0,
(4*a^2*Sqrt[-1 + b^2/a^2]*EllipticE[
1 - b^2/a^2])/Sqrt[-a^2 + b^2],
Integrate[Sqrt[a^2 + (-a^2 + b^2)*Sin[t]^2],
{t, 0, 2*Pi}]]
Someone can explane me this difference?
Thanks,
Raf.
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