Re: Integrate is driving me crazy, please help!

*To*: mathgroup at smc.vnet.net*Subject*: [mg56207] Re: Integrate is driving me crazy, please help!*From*: Peter Pein <petsie at arcor.de>*Date*: Tue, 19 Apr 2005 04:55:05 -0400 (EDT)*References*: <d3vn1h$jm9$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Jim Martin 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 > > Hi Jim, 1. use square brackets for functions: Cos[f] instead of Cos(f). 2. use Pi instead of pi. How did you get /any/ result with these typos? Please download http://people.freenet.de/Peter_Berlin/Mathe/Integral/Integral.nb or have just a look at http://people.freenet.de/Peter_Berlin/Mathe/Integral/Integral.html -- Peter Pein Berlin