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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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