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Re: A buglooking behavior during integration
Posted:
Feb 28, 2013 9:25 PM


This does appear to be a bug. Two other examples (Mathematica 8.0.4):
In: Integrate[UnitStep[(1+Cos[ArcTan[x, y]])Sqrt[x^2+y^2]], {x, Infinity, Infinity}, {y, Infinity, Infinity}] Out: 0
In: Integrate[UnitStep[Cos[3*ArcTan[x, y]]Sqrt[x^2+y^2]], {x, Infinity, Infinity}, {y, Infinity, Infinity}] Out: 0
Alex
On Wed, 27 Feb 2013, Alexei Boulbitch wrote:
> Dear community, > > I would like to report a strange behaviour, that looks most of all like a bug. > > The integral of the UnitStep of some function > > Integrate[ > UnitStep[Sqrt[Sqrt[x^2 + y^2] + x]  > 0.7 Sqrt[x^2 + y^2]], {x, Infinity, Infinity}, {y, Infinity,Infinity}] > > 0 > > returns zero as you see, though the function under the integral is 1 within some domain in the form of a cardioid, and zero outside of it. To make it sure evaluate this: > > Plot3D[UnitStep[ > Sqrt[Sqrt[x^2 + y^2] + x]  0.7 Sqrt[x^2 + y^2]], {x, 3, 5}, {y, 3, 5}] > > The integral must be positive, therefore. > > Taking the numerical value of the same integral one finds a finite positive value: > > NIntegrate[ > UnitStep[Sqrt[Sqrt[x^2 + y^2] + x]  > 0.7 Sqrt[x^2 + y^2]], {x, Infinity, Infinity}, {y, Infinity, Infinity}] > > 19.6268 > > Is it indeed a bug? > > Regards, Alexei > > > Alexei BOULBITCH, Dr., habil. > IEE S.A. > ZAE Weiergewan, > 11, rue Edmond Reuter, > L5326 Contern, LUXEMBOURG > > Office phone : +35224542566 > Office fax: +35224543566 > mobile phone: +49 151 52 40 66 44 > > email: alexei.boulbitch@iee.lu > > > >



