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MathGroup Archive 2005

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Integrate is driving me crazy, please help!

  • To: mathgroup at smc.vnet.net
  • Subject: [mg56184] Integrate is driving me crazy, please help!
  • From: Jim Martin <jim.martin at utah.edu>
  • Date: Mon, 18 Apr 2005 03:08:44 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

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



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