Integrate?

*To*: "mathgroup" <mathgroup at yoda.ncsa.uiuc.edu>*Subject*: Integrate?*From*: "WILLIAM M. GOLDING" <golding at ccf4.nrl.navy.mil>*Date*: 6 Nov 90 22:00:00 EST

In a previous posting concerning this integration flaw in Mathematica which Robert Staerk recently brought up, Integrate[Sqrt[2-2 Cos[x]],{x,0,2 Pi}] =?= 0 Jeffrey Golden mentions an integral which he has just been able to get Macsyma to do correctly. The integral he mentions is Integrate[Sqrt[x + 1/x -2],{x,0,1}] = 4/3 . Jeff says that Macsyma used to give the result as -4/3, which by the way is what Mathematica gives. I just wanted to point out the similarity between these two integrals. If in the second integral x is replaced by E^(I x) the first integral is almost obtained except for a phase factor and for the integration contour which I don't quite know how to interpret at the moment. Anyways I just thought I'd mention the connection since Jeff implied that the second form has been corrected in Macsyma. Mike Golding Email golding at ccf.nrl.navy.mil