Re: Bug in Integrate?

*To*: mathgroup at smc.vnet.net*Subject*: [mg28775] Re: [mg28744] Bug in Integrate?*From*: BobHanlon at aol.com*Date*: Sat, 12 May 2001 01:36:42 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

There is a problem. Use numerical integration f[x_] := Abs[x^4 - 4x^3 + 2x^2 + 1]; Plot[f[x], {x, 0, 4}]; NIntegrate[f[x], {x, 0, 4}] \!\(\*FormBox[ RowBox[{\(NIntegrate::"ncvb"\), \(\(:\)\(\ \)\), "\<\"NIntegrate failed to \ converge to prescribed accuracy after \\!\\(TraditionalForm\\`7\\) recursive \ bisections in \\!\\(TraditionalForm\\`x\\) near \\!\\(TraditionalForm\\`x\\) \ = \\!\\(TraditionalForm\\`3.390625`\\).\"\>"}], TraditionalForm]\) 23.529273252933095 lim = Partition[ Flatten[{0, Select[x /. Simplify[Solve[x^4 - 4x^3 + 2x^2 + 1 == 0, x]], Element[#, Reals] && 0<=#<=4&], 4}], 2, 1]; Plus @@ (NIntegrate[f[x], {x, #[[1]], #[[2]]}]& /@ lim) 23.529273034761246 Bob Hanlon In a message dated 2001/5/11 8:18:14 PM, rcwil at win.tue.nl writes: >I am a very enthusiastic Mathematica user. >Mathematica has become faster, but what I like more is reliable integration. >In Mathematica 4.1 evaluating the expression > >Integrate[Abs[x^4 - 4x^3 + 2x^2 + 1], {x, 0, 4}] > >gives me -14/5 as the result, what of course can not be correct. >Or am I overlooking something? >