Re: Help needed - Mathematica code
- To: mathgroup at smc.vnet.net
- Subject: [mg122988] Re: Help needed - Mathematica code
- From: "Tetsu Tetsu.HDD" <tetsu.hdd at gmail.com>
- Date: Sat, 19 Nov 2011 06:47:48 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <ja5f83$6bm$1@smc.vnet.net>
On 11=E6=9C=8818=E6=97=A5, =E5=8D=88=E5=BE=8C8:23, Daniel Lichtblau <d... at wolfram.com> wrote:
> ----- Original Message -----
> > From: "Tetsu Tetsu.HDD" <tetsu.... at gmail.com>
> > To: mathgr... 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},
> =C2 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*
> =C2 =C2 b*((-1 + c)/a)^(1/b)*(d/c)^(1/b))/(-1 + 2*b), b > 1/2]
>
> Daniel Lichtblau
> Wolfram Research
Dear Daniel Lichtblau
Your code worked perfectly.
Many thanks!!!!!
T