       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?
>
>
> T

If I understand correctly, then it might be that you want something along the lines below.

In:=
y[x_] := y /. First[Solve[c - (y/(d - x*y^b))*x*y^(b - 1) == 1, y]]

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

During evaluation of In:= Solve::ifun:Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. >>

Out= 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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