Re : Integrate is driving me crazy, please help!

*To*: mathgroup at smc.vnet.net*Subject*: [mg56197] Re : [mg56184] Integrate is driving me crazy, please help!*From*: "Jaccard Florian" <Florian.Jaccard at he-arc.ch>*Date*: Tue, 19 Apr 2005 04:54:53 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hello Jim, It is in fact a beginner-problem... The arguments of functions must be [] , not () ... So you should write : expr = Integrate[hillb*((f0 + hilla)/(2*Pi*f*a*Cos[ArcSin[x/a]] + hillb)) - hilla, {x, -a, a}] Which gives an answer like you expect... expr2 = Simplify[expr, {a, hilla, f, hillb, f0} > 0]; expr2 /. {hilla -> 3, hillb -> 50, f0 -> 8, a -> 1, f -> 1.} gives : 14.037200672826035 + 0.*I Don't be afraid of the complex numbers, the imaginary part is 0... Regards F.Jaccard -----Message d'origine----- De : Jim Martin [mailto:jim.martin at utah.edu] Envoyé : lundi, 18. avril 2005 09:09 À : mathgroup at smc.vnet.net Objet : [mg56184] Integrate is driving me crazy, please help! Hello Mathematica Experts: I am a biomechanist and work mostly in the area of muscle contraction. I do a lot of numerical computations using excel, but right now I need an analytical solution that represents force as a function of position integrated over a shortening amplitude. I downloaded a trial version of Mathematica and have tried to obtain a solution for this: Integrate[(hillb*((f0 + hilla)/(2*pi*f*a*Cos(ArcSin(x/a)) + hillb))) - hilla, {x, -a, a}] Mathematica returns this: (-4 a ArcSin Cos f hilla pi + (f0 + hilla) hillb (-Log[hillb - 2 a ArcSin Cos f pi] + Log[hillb + 2 a ArcSin Cos f pi]))/(4 a ArcSin Cos f pi) I know the line wrap makes this hard to read so please feel free to email me and I can send you the output as a picture. In a sample data set, hilla=3, hillb=50, f0=8, a=1, f=1 I can numerically integrate this function and obtain a value for that sample data set of 14.04. When I put those sample values into the solution that Mathematica produces, I get 10.01. Can any of you please give a hand here? I must be making some simple Mathematica-beginner error but I just can't see it. In Mathematica, Log is Log to base e, right (LN in excel)? Did I use variables that have intrinsic functions in Mathematica? Maybe I am misunderstanding the output with regard to implicit parentheses etc. Any help appreciated! Thanks, Jim