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Re: Dificulty on Integrate function!

  • To: mathgroup at smc.vnet.net
  • Subject: [mg96971] Re: [mg96934] Dificulty on Integrate function!
  • From: DrMajorBob <btreat1 at austin.rr.com>
  • Date: Sat, 28 Feb 2009 06:44:13 -0500 (EST)
  • References: <200902271116.GAA21652@smc.vnet.net>
  • Reply-to: drmajorbob at bigfoot.com

You want to integrate an equation (but equations CAN'T be integrated) and  
anyway, you haven't given us an equation. (Just an expression.)

Indefinite integration of that expression w.r.t. b, c, and d would still  
give a function of FIVE variables -- not just t and a.

And definite integration w.r.t. b, c, and d probably isn't possible,  
either -- I'm pretty sure there's no closed form expression for it, when t  
and a are undefined (variable).

So you'll have to rein in your wants, here. What CAN be done (maybe) is  
something like

f[t_, a_][b_, c_,
    d_] = (5.985857026794833*^-14*(14 + c)^2.37*
      E^(-0.0003630681026445808*(-50.29 + b)^2 - c/41 -
         0.0003125*(-43.7 + d)^2 - b/d + t/d -
         1.1985780806058064*^-6*(-3535.42 +
             c + ((a - c)*E^((-b + t)/d))/(t/b)^(b/d))^2))/(t/b)^(b/
       d);
g[t_?NumericQ, a_?NumericQ] :=
  NIntegrate[f[t, a][b, c, d], {b, 0, 170.}, {c, 0, 400.}, {d, 0, 170.}]

g[0.5, 0.3]

But, if you execute that, you'll see that NIntegrate has convergence  
problems.

Experiment with various options to NIntegrate and maybe, for some values  
of t and a, you can get convergence.

Your expression has t in a couple of denominators, but you want to  
integrate with t from 0 to (doesn't matter what). That in itself may make  
convergence impossible. So changing the lower limit might help a lot.

Bobby

On Fri, 27 Feb 2009 05:16:04 -0600, <negedea at googlemail.com> wrote:

> Dear all,
>
> I got a problem in integrating the expression (given below in input
> form) on Mathematica. Please give me some hints or a way around to get
> the solutions. . I want to integrate the equation  with respect to b,
> c, and d. So that I get an equation only in terms of t and a. I tried
> to use Integrate function in Mathematica both in the form of definite
> and indefinite integral but it could not turn out the result. If the
> indefinite integral is not working the ranges of integration for
> definite integral shall be the following {b, 0, 170}, {c, 0, 400} and
> {d, 0,170}.
>
> (5.985857026794833*^-14*(14 + c)^2.37*E^(-0.0003630681026445808*
> (-50.29 + b)^2 - c/41 - 0.0003125*(-43.7 + d)^2 - b/d + t/d -
> 1.1985780806058064*^-6*(-3535.42 + c + ((a - c)*E^((-b + t)/d))/(t/b)^
> (b/d))^2))/(t/b)^(b/d)
>
> Please please help me. If I could not get this solution I have to
> discard so many things I spent considerable time on!
>
> Thanking you in advance.
>
> Negede
>



-- 
DrMajorBob at bigfoot.com


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