# Problem with integrate and assumptions

Posted 15 days ago
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 Dear all,I am struggling to understand why the following integration: Integrate[t*BesselJ[0,k*r]*(-HeavisideTheta[t-r/a]+HeavisideTheta[t-r/b])/r^2,{r,0,Infinity},Assumptions->{k>=0,a>0,b>0,a>b,t>=0}] Is not giving the same result as (notice that only the assumption about t>0 or t>=0 has changed): Integrate[t*BesselJ[0,k*r]*(-HeavisideTheta[t-r/a]+HeavisideTheta[t-r/b])/r^2,{r,0,Infinity},Assumptions->{k>=0,a>0,b>0,a>b,t>0}] I am expecting the result to be non-zero, because this integration arise from calculating the Fourier transform of a non-zero function in 2D. Do you have any ideas why the calculation gives two different results?I am using Mathematica Version 12.2.0.0 on Mac. Attachments:
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Posted 9 days ago
 Hello Pierre,with my stone-age-old Version 7 both integrals give zero.Perhaps you should check this numerically. Your integrand is, let's say, somewhat special (for a > b I wrote a = b + x and x >0 ). But I am quite sure that there are combinations of the parameters that the integral is different from zero. Manipulate[ Plot[Evaluate[ t*BesselJ[0, k*r]*(-HeavisideTheta[t - r/(b + x)] + HeavisideTheta[t - r/b])/ r^2], {r, 0, 5}, PlotRange -> {-.2, .2}], {t, 0, 5}, {x, .01, 5}, {k, 0, 5}, {b, .1, 5}] 
Posted 9 days ago
 Dear Hans, Thank you a lot for your answer. I will try what you said. I am also quite sure this integral is non-zero except for negative t.
Posted 8 days ago
 I will file a bug report for this.
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