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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: [mg56209] Re: [mg56184] Integrate is driving me crazy, please help!
  • From: Chris Chiasson <chris.chiasson at gmail.com>
  • Date: Tue, 19 Apr 2005 04:55:12 -0400 (EDT)
  • References: <200504180708.DAA20024@smc.vnet.net>
  • Reply-to: Chris Chiasson <chris.chiasson at gmail.com>
  • Sender: owner-wri-mathgroup at wolfram.com

Try this instead:
Integrate[(hillb*((f0 + hilla)/(2*
        Pi*f*a*Cos[ArcSin[x/a]] + hillb))) - hilla, {x, -a, a}]
% /. {hilla -> 3, hillb -> 50, f0 -> 8, a -> 1, f -> 1}
% // N

On 4/18/05, Chris Chiasson <chris.chiasson at gmail.com> wrote:
> Of course, that might be expected when none of the fuctions have their
> arguments specified with brackets, as they are supposed to...
> 
> On 4/18/05, Chris Chiasson <chris.chiasson at gmail.com> wrote:
> > In Mathematica 5.0, if I evaluate the else branch (not shown above) of
> > the output from the above mentioned integration command, the kernel
> > crashes.
> >
> > On 4/18/05, Jim Martin <jim.martin at utah.edu> 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
> > >
> > >
> >
> > --
> > Chris Chiasson
> > Kettering University
> > Mechanical Engineering
> > Graduate Student
> > 1 810 265 3161
> >
> 
> --
> Chris Chiasson
> Kettering University
> Mechanical Engineering
> Graduate Student
> 1 810 265 3161
> 


-- 
Chris Chiasson
Kettering University
Mechanical Engineering
Graduate Student
1 810 265 3161


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