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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: [mg56190] Re: Integrate is driving me crazy, please help!
  • 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 
> 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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