Re: Integrate is driving me crazy, please help!

*To*: mathgroup at smc.vnet.net*Subject*: [mg56205] Re: [mg56184] Integrate is driving me crazy, please help!*From*: DrBob <drbob at bigfoot.com>*Date*: Tue, 19 Apr 2005 04:55:03 -0400 (EDT)*References*: <200504180708.DAA20024@smc.vnet.net>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

Integrate[hillb*((f0 + hilla)/ (2*Pi*f*a*Cos[ArcSin[x/a]] + hillb)) - hilla, {x, -a, a}] (-4*a^2*f*hilla*Pi* Sqrt[hillb^2 - 4*a^2*f^2* Pi^2] + a*f0*hillb*Pi* Sqrt[hillb^2 - 4*a^2*f^2* Pi^2] + a*hilla*hillb*Pi* Sqrt[hillb^2 - 4*a^2*f^2* Pi^2] + 2*a*(f0 + hilla)* hillb^2*ArcTan[(2*a*f*Pi)/ Sqrt[hillb^2 - 4*a^2*f^2* Pi^2]] - I*Sqrt[a^2]* (f0 + hilla)*hillb^2* Log[-((I*Sqrt[a^2]*hillb)/ (2*a*Sqrt[hillb^2 - 4*a^2*f^2*Pi^2]))] + I*Sqrt[a^2]*f0*hillb^2* Log[(I*Sqrt[a^2]*hillb)/ (2*a*Sqrt[hillb^2 - 4*a^2*f^2*Pi^2])] + I*Sqrt[a^2]*hilla*hillb^2* Log[(I*Sqrt[a^2]*hillb)/ (2*a*Sqrt[hillb^2 - 4*a^2*f^2*Pi^2])])/ (2*a*f*Pi*Sqrt[hillb^2 - 4*a^2*f^2*Pi^2]) % /. {hilla -> 3, hillb -> 50, f0 -> 8, a -> 1, f -> 1} (1/(2*Pi*Sqrt[2500 - 4*Pi^2]))* (538*Pi*Sqrt[2500 - 4*Pi^2] + 55000*ArcTan[(2*Pi)/ Sqrt[2500 - 4*Pi^2]] - 27500*I*Log[-((25*I)/ Sqrt[2500 - 4*Pi^2])] + 27500*I*Log[(25*I)/ Sqrt[2500 - 4*Pi^2]]) N[%] 14.037200672826035 + 0.*I Bobby On Mon, 18 Apr 2005 03:08:44 -0400 (EDT), Jim Martin <jim.martin at utah.edu> wrote: > 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 > > > > > -- DrBob at bigfoot.com

**References**:**Integrate is driving me crazy, please help!***From:*Jim Martin <jim.martin@utah.edu>