Re: Bug of Integrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg82725] Re: Bug of Integrate*From*: "David W.Cantrell" <DWCantrell at sigmaxi.net>*Date*: Tue, 30 Oct 2007 03:20:57 -0500 (EST)*References*: <fg4dfv$6c3$1@smc.vnet.net>

Miguel <misvrne at gmail.com> wrote: > When I try to calculate the integral > > Integrate[Sqrt[1/Cos[t]^2]*3*Cos[t],{t,0,2Pi}] Mathematica 6.0.1 > yields -6*Pi. If so, then that is clearly a bug. But in version 5.2, the result is correct: In[1]:= Integrate[Sqrt[1/Cos[t]^2]*3*Cos[t],{t,0,2Pi}] Out[1]= 0 > Simplifying the expresion resultrs Integrate[3,{t,0,2*Pi}] and It is > clear that the correct solution is 6*Pi. No. Simplifying the integrand does not give 3, rather In[2]:= Simplify[Sqrt[1/Cos[t]^2]*3*Cos[t], Element[t,Reals]] Out[2]= 3 Abs[Sec[t]] Cos[t] which BTW is the same as 3 Sign[Cos[t]] for real t except when Cos[t]==0. However, related to the above, version 5.2 does give an incorrect result for a definite integral with a symbolic real limit. Whether this error still exists in version 6, I don't know: In[3]:= Assuming[Element[x,Reals],Integrate[3*Sign[Cos[t]],{t,0,x}]] Out[3]= 3 If[x > 0, x Abs[Cos[x]] Sec[x], Integrate[Sign[Cos[t]], {t, 0, x}, Assumptions -> x <= 0]] The above is incorrect for x > Pi/2. A correct result would have been 3 Sign[Cos[x]] (x - Pi Floor[x/Pi + 1/2]) for all real x. David W. Cantrell