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.