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Re: Help needed - Mathematica code

  • To: mathgroup at smc.vnet.net
  • Subject: [mg122948] Re: Help needed - Mathematica code
  • From: Daniel Lichtblau <danl at wolfram.com>
  • Date: Fri, 18 Nov 2011 06:22:21 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com


----- 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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