Re: problem getting the area under a parmetric curve

*To*: mathgroup at smc.vnet.net*Subject*: [mg52860] Re: problem getting the area under a parmetric curve*From*: Roger Bagula <tftn at earthlink.net>*Date*: Wed, 15 Dec 2004 04:26:20 -0500 (EST)*References*: <cpauof$ipf$1@smc.vnet.net>*Reply-to*: tftn at earthlink.net*Sender*: owner-wri-mathgroup at wolfram.com

Another of these distribution like pairs is: {(1-t^7)/(1+t^7),2^1/6*t*(7+35*t^14+21*t^28+t^42)^1/7/(1+t^7)} When fitted in the previous area programs, my computer doesn't compute the area of the normalization factor. n=6, 8 are again a squared circles. It appears that these can be done for general n case and the odd ones give the distributioin like parametric. Roger Bagula wrote: >I worked on this late last night. >I had trouble even having the curve well defined >finding the area under it. >I used the symmetry to integrate the side >that was easiest. There is only one real zero for the x parametric >in t which helps. >An Infinite integral does appear to exist for the distribution. > >(* cubic pair and rotated distribution function*) >Clear[x0,y0,ang,x,y,z] >x0=(1-t^3)/(1+t^3) >y0=2^(1/3)*t*(3+t^6)^(1/3)/(1+t^3) >ParametricPlot[{x0,y0},{t,-2*Pi,2*Pi}] >Simplify[x0^3+y0^3] >ang=4 >x=Cos[Pi/ang]*x0-Sin[Pi/ang]*y0 >y=Cos[Pi/ang]*y0+Sin[Pi/ang]*x0 >NSolve[x==0,t] >N[y/.t->0.486313] >N[x/.t->0.486313] >ParametricPlot[{x,y},{t,-2*Pi,2*Pi}] >f[t_]=x >norm=Integrate[-y*f'[t],{t,0.486313,Infinity}] >a0=N[2*norm] >g1=ParametricPlot[{x,y}/(a0),{t,-2*Pi,2*Pi}] >g2=Plot[Exp[-t^2/2]/Sqrt[2*Pi],{t,-Pi,Pi}] >Show[{g1,g2}] >Respectfully, Roger L. Bagula > >tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 : >alternative email: rlbtftn at netscape.net >URL : http://home.earthlink.net/~tftn > > > -- Respectfully, Roger L. Bagula tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 : alternative email: rlbtftn at netscape.net URL : http://home.earthlink.net/~tftn

**Follow-Ups**:**Re: Re: problem getting the area under a parmetric curve***From:*Daniel Lichtblau <danl@wolfram.com>