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