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MathGroup Archive 2005

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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


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