Re: implicit function
- To: mathgroup at smc.vnet.net
- Subject: [mg109693] Re: implicit function
- From: cinnabar <kolbasa.sapiens at gmail.com>
- Date: Wed, 12 May 2010 07:33:30 -0400 (EDT)
- References: <hsbbg7$jmo$1@smc.vnet.net>
Hello, Alexey!
The first and most simple way to do this that came to my mind is:
x[b_, t_] = (Sqrt[3] - Sqrt[(3 - 2 b^2*Sin[t]^2)])/(Sqrt[3] +
Sqrt[(3 - 2 b^2*Sin[t]^2)]);
Phi[x1_] = (1 + x1)^3 (1 - x1) Exp[-x1];
And then just plot the equation line with ContourPlot. Note that
NIntegrate is used to avoid computing integral in analytic form:
ContourPlot[
NIntegrate[(Phi[x[b, tt]] Sin[tt]), {tt, t1, Pi/2}] ==
1/2 NIntegrate[(Phi[x[b, tt]] Sin[tt]), {tt, 0, Pi/2}],
{b, 0, 1}, {t1, 0, Pi/2}, MaxRecursion -> 10]
ContourPlot can be used intrinsically to plot equations, as you can
see in help section on this function. Mathematica 7 has nice
Documentation Center, which is strongly suggested to read when a
question arises on a function definition, arguments, etc. It has a lot
of examples too and many-many guidelines, tutorials, demos etc.
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