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Re: Help needed - Mathematica code

  • To: mathgroup at smc.vnet.net
  • Subject: [mg123026] Re: Help needed - Mathematica code
  • From: Barrie Stokes <Barrie.Stokes at newcastle.edu.au>
  • Date: Mon, 21 Nov 2011 04:26:01 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201111181122.GAA06449@smc.vnet.net>

Daniel's (successful) integration is of x*y[x], whereas I read the original posting as wanting the integration of x*y[x]^b,

in which case

Integrate[ x*y[x]^b, {x, 0, a}, 
  Assumptions -> {a > 0, 1 > b > 0, c > 0, d > 0} ]

produces the (slightly simpler and unconditional on b) output

(a ((-1 + c)^(1/b))^b d)/c

Barrie

>>> On 18/11/2011 at 10:22 pm, in message <201111181122.GAA06449 at smc.vnet.net>,
Daniel Lichtblau <danl at wolfram.com> wrote:

> 
> ----- Original Message -----
>> From: "Tetsu Tetsu.HDD" <tetsu.hdd at gmail.com>
>> To: mathgroup at smc.vnet.net 
>> Sent: Thursday, November 17, 2011 5:04:08 AM
>> Subject: Help needed - Mathematica code
>> 
>> Hi,
>> 
>> I would greatly appreciate if anyone can help me out of this problem.
>> 
>> To explain my problem, I will use LaTeX code.
>> 
>> Given a>0, 1>b>0, c>0 and d>0, I want to calculate the following
>> 
>> \int_0^a X Y(X)^b dX
>> 
>> where Y(X) is defined by
>> 
>> (c - \frac{Y}{d-X Y^b}) X Y^{b-1}=1
>> 
>> Can you tell me Mathematica codes for this problem?
>> 
>> Thank you in advance.
>> 
>> T
> 
> If I understand correctly, then it might be that you want something along 
> the lines below.
> 
> In[164]:= 
> y[x_] := y /. First[Solve[c - (y/(d - x*y^b))*x*y^(b - 1) == 1, y]]
> 
> In[166]:= Integrate[x*y[x], {x, 0, a}, 
>  Assumptions -> {a > 0, 1 > b > 0, c > 0, d > 0}]
> 
> During evaluation of In[166]:= Solve::ifun:Inverse functions are being used 
> by Solve, so some solutions may not be found; use Reduce for complete 
> solution information. >>
> 
> Out[166]= ConditionalExpression[(a^2*
>     b*((-1 + c)/a)^(1/b)*(d/c)^(1/b))/(-1 + 2*b), b > 1/2]
> 
> Daniel Lichtblau
> Wolfram Research
>  




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