• To: mathgroup at smc.vnet.net
• 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
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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