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Re: Integrate is driving me crazy, please help!
*To*: mathgroup at smc.vnet.net
*Subject*: [mg56193] Re: [mg56184] Integrate is driving me crazy, please help!
*From*: Bob Hanlon <hanlonr at cox.net>
*Date*: Tue, 19 Apr 2005 04:54:49 -0400 (EDT)
*Reply-to*: hanlonr at cox.net
*Sender*: owner-wri-mathgroup at wolfram.com
Use square brackets for all functions
asmp={Element[{a,f,f0,hilla,hillb}, Reals],
a>0,hillb>0};
soln = Simplify[Integrate[
(hillb*((f0+hilla)/
(2*Pi*f*a*Cos[ArcSin[x/a]]+hillb)))-
hilla,{x,-a,a}],asmp]
(1/(2*f*Pi*Sqrt[hillb^2 - 4*a^2*f^2*Pi^2]))*
(2*(f0 + hilla)*ArcTan[(2*a*f*Pi)/Sqrt[hillb^2 - 4*a^2*f^2*Pi^2]]*hillb^2 -
I*(f0 + hilla)*Log[-(I/(2*Sqrt[hillb^2 - 4*a^2*f^2*Pi^2]))]*hillb^2 +
I*f0*Log[I/(2*Sqrt[hillb^2 - 4*a^2*f^2*Pi^2])]*hillb^2 +
I*hilla*Log[I/(2*Sqrt[hillb^2 - 4*a^2*f^2*Pi^2])]*hillb^2 +
f0*Pi*Sqrt[hillb^2 - 4*a^2*f^2*Pi^2]*hillb + hilla*Pi*Sqrt[hillb^2 -
4*a^2*f^2*Pi^2]*
hillb - 4*a*f*hilla*Pi*Sqrt[hillb^2 - 4*a^2*f^2*Pi^2])
Simplify[soln/.{hilla->3,hillb->50,f0->8,a->1,f->1}]
269 - 6875/Sqrt[625 - Pi^2] + (13750*ArcTan[Pi/Sqrt[625 - Pi^2]])/
(Pi*Sqrt[625 - Pi^2])
%//N
14.0372
Bob Hanlon
>
> From: Jim Martin <jim.martin at utah.edu>
To: mathgroup at smc.vnet.net
> Date: 2005/04/18 Mon AM 03:08:44 EDT
> To: mathgroup at smc.vnet.net
> Subject: [mg56193] [mg56184] Integrate is driving me crazy, please help!
>
> 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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