• To: mathgroup at smc.vnet.net
• From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
• Date: Tue, 19 Apr 2005 04:54:46 -0400 (EDT)
• Organization: Uni Leipzig
• References: <d3vn1h\$jm9\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

first of all you should fix you input, Mathematica
uses []
for *all* function brakets and pi is Pi

res=Integrate[
(hillb*((f0 + hilla)/
(2*Pi*f*a*Cos[ArcSin[x/a]] + hillb))) - hilla,
{x, -a, a}]

than you should do

tmp = FullSimplify[res, Element[{a, f, hillb,
hilla}, Reals]];

and help Mathematica with your Log[] arguments

tmp //. a_*Log[b_] :> Log[b^a] //. Log[a_] +
Log[b_] :> Log[a*b]

than you have the solution, you expect.

Regards
Jens

"Jim Martin" <jim.martin at utah.edu> schrieb im
Newsbeitrag news:d3vn1h\$jm9\$1 at smc.vnet.net...
> 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
> 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
> 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
>
>

```