Re: Integrate is driving me crazy, please help!

*To*: mathgroup at smc.vnet.net*Subject*: [mg56193] Re: [mg56184] Integrate is driving me crazy, please help!*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Tue, 19 Apr 2005 04:54:49 -0400 (EDT)*Reply-to*: hanlonr at cox.net*Sender*: owner-wri-mathgroup at wolfram.com

Use square brackets for all functions asmp={Element[{a,f,f0,hilla,hillb}, Reals], a>0,hillb>0}; soln = Simplify[Integrate[ (hillb*((f0+hilla)/ (2*Pi*f*a*Cos[ArcSin[x/a]]+hillb)))- hilla,{x,-a,a}],asmp] (1/(2*f*Pi*Sqrt[hillb^2 - 4*a^2*f^2*Pi^2]))* (2*(f0 + hilla)*ArcTan[(2*a*f*Pi)/Sqrt[hillb^2 - 4*a^2*f^2*Pi^2]]*hillb^2 - I*(f0 + hilla)*Log[-(I/(2*Sqrt[hillb^2 - 4*a^2*f^2*Pi^2]))]*hillb^2 + I*f0*Log[I/(2*Sqrt[hillb^2 - 4*a^2*f^2*Pi^2])]*hillb^2 + I*hilla*Log[I/(2*Sqrt[hillb^2 - 4*a^2*f^2*Pi^2])]*hillb^2 + f0*Pi*Sqrt[hillb^2 - 4*a^2*f^2*Pi^2]*hillb + hilla*Pi*Sqrt[hillb^2 - 4*a^2*f^2*Pi^2]* hillb - 4*a*f*hilla*Pi*Sqrt[hillb^2 - 4*a^2*f^2*Pi^2]) Simplify[soln/.{hilla->3,hillb->50,f0->8,a->1,f->1}] 269 - 6875/Sqrt[625 - Pi^2] + (13750*ArcTan[Pi/Sqrt[625 - Pi^2]])/ (Pi*Sqrt[625 - Pi^2]) %//N 14.0372 Bob Hanlon > > From: Jim Martin <jim.martin at utah.edu> To: mathgroup at smc.vnet.net > Date: 2005/04/18 Mon AM 03:08:44 EDT > To: mathgroup at smc.vnet.net > Subject: [mg56193] [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 > > >