[bug]Calculate a conditional reintegration

04112019, 06:30 PM
(This post was last modified: 04112019 06:31 PM by parisse.)
Post: #2




RE: [bug]Calculate a conditional reintegration
You have been warned that some checks were not done, it's not that surprising that the answer is wrong. Now ask yourself, how can I solve this exacty in an algorithm? You must find an antiderivative of min(x^2,y^2), and to do that you must rewrite min(x^2,y^2) algebraically, which is
x^2+y^2(x^2y^2)*sign(x^2y^2) then you can integrate w.r.t. y, since sign is constant by interval, g:=int((x^2+y^2)/2abs(x^2y^2)/2,y) giving (y^3/3+x^2*y)/2sign(x^2y^2)*(y^3/3+x^2*y)/2 Then you would substitute between 0 and 1, h:=g(y=1)g(y=0) but that's not sufficient, because you should take care of the points where sign(x^2y^2) is not continuous and add the right/left limit difference. And that means solving an equation. I have decided not to solve it if it is a parametric equation (here the equation in y depends on x), because it would raise endless loops or fail, instead I issue a warning. Let's correct it : h1:=limit(g,y,x,1)limit(g,y,x,1) We must correct the integral by substracting this step, for x in [0,1], i.e substract int(h1,x,0,1)=1/6. I guess mathematica does more complete checks, but at some point, you will certainly be able to make it return wrong answer as well. I do not have a staff of people trying a lot of weird integrals to improve/implement automatic checks, you will have to be a little bit more smart, and fix answers when you have been warned. 

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[bug]Calculate a conditional reintegration  yangyongkang  04112019, 12:57 PM
RE: [bug]Calculate a conditional reintegration  parisse  04112019 06:30 PM

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