Re: Integrate is driving me crazy, please help!

*To*: mathgroup at smc.vnet.net*Subject*: [mg56216] Re: Integrate is driving me crazy, please help!*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Tue, 19 Apr 2005 04:55:35 -0400 (EDT)*Organization*: The University of Western Australia*References*: <d3vn1h$jm9$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <d3vn1h$jm9$1 at smc.vnet.net>, 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}] Instead of 2*pi*f*a*Cos(ArcSin(x/a)) you mean 2 Pi f a Cos[ArcSin[x/a]] + hillb (In StandardForm, pi needs to be capitalised and square brackets are required). > 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) In this output you will see expressions like ArcSin Cos f pi which make no sense. Correcting the integrand, and massaging the result from Integrate, I get ((f0 + hilla) hillb (Pi (Sqrt[hillb^2 - 4 a^2 f^2 Pi^2] - hillb) + 2 hillb ArcTan[(2 a f Pi)/Sqrt[hillb^2 - 4 a^2 f^2 Pi^2]]))/ (2 f Pi Sqrt[hillb^2 - 4 a^2 f^2 Pi^2]) - 2 a hilla > In a sample data set, hilla=3, hillb=50, f0=8, a=1, f=1 For this dataset, numerical evaluation gives 14.0372. > I can numerically integrate this function and obtain a value for that > sample data set of 14.04. But how did you do this and get this correct result if you used the wrong integrand? > 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. Wrong type of parentheses. If you use TraditionalForm for input and output (Cell | Default Input FormatType, etc.) you _can_ enter expressions using () instead of []. Cheers, Paul -- Paul Abbott Phone: +61 8 6488 2734 School of Physics, M013 Fax: +61 8 6488 1014 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul