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A bug-looking behavior during integration
Posted:
Feb 27, 2013 11:42 PM
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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,
L-5326 Contern, LUXEMBOURG
Office phone : +352-2454-2566
Office fax: +352-2454-3566
mobile phone: +49 151 52 40 66 44
e-mail: alexei.boulbitch@iee.lu
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