How to do Double numerical integration with a variable limits

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Abdulaziz Al-Amodi
评论： Abdulaziz Al-Amodi 2022-9-8
Can someone please help me in doing numerical integration on the following function, I want to do double numerical integration with respect to y and x, such that the final answer will be a function of z only. Also the limit of integration is not a constant, it is basically something like (x-y, x+y), not sure if there exist a way to do this, can someone please advise me on how to proceed?
Thank you
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Torsten
Torsten 2022-9-4
@John D'Errico @Walter Roberson
The integral (once it is correctly written) could be considered as a function of z. Then numerical integration can be carried out.
Abdulaziz Al-Amodi
Abdulaziz Al-Amodi 2022-9-6
编辑：Abdulaziz Al-Amodi 2022-9-6
z is always positive, I made a mistake when I wrote -inf, was just trying to understand the implementation of it.
I found 'vpaintegral' and it looks promising but it is very slow to compute.
Thank you for your help

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Matt J
Matt J 2022-9-6
编辑：Matt J 2022-9-6
Ran in:
I'll demonstrate for a simpler function. The technique is the same regardless of what function we're integrating.
F=@(x,y,z) x.^2+y.^2+z.^2; %The input function to be integrated
Iyz=@(y,z)integral( vect(@(q)F(q,y,z)), z-y,z+y); %partial integral w.r.t. x
Iz=@(z) integral( vect(@(q)Iyz(q,z)) , 0,z); %partial integral w.r.t. y
Iz(1)
ans = 2.6667
function fun=vect(fun)
%vectorize a non-vectorized function
fun=@(x) arrayfun(fun,x);
end
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Torsten
Torsten 2022-9-8
编辑：Torsten 2022-9-8
Yes, the square root in the denominator is quite ambitious ... When it gives real values and when it is different from 0 ... To take care of it in the integration limits for x,y and z won't be easy - be it with or without Mathematica.

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