       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:=
Integrate[Sqrt[a^2*Cos[t]^2 + b^2*Sin[t]^2],
{t, 0, 2*Pi}, Assumptions->{Im[a]==0, Im[b]==0}]

Out=
0

....but written in another way, it's right:

In:=
Integrate[Sqrt[a^2 + (b^2 - a^2)*Sin[t]^2],
{t, 0, 2*Pi}, Assumptions ->
{Im[a] == 0, Im[b] == 0}]

Out=
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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