How to use an integral inside another integral

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may
may on 19 Sep 2013
Commented: may on 27 Sep 2013
I have the following code:
function [answer]=find_integral2(z)
F=@(y) find_integral(z-y).*find_integral(y);
answer= integral(F,-Inf,Inf);
end
function [answer]=find_integral(u)
F = @(x)normpdf(x).*normpdf(u./x);
answer= integral(F,-Inf,Inf);
end
When I call the function find_integral2(4), I get the following error:
Error using ./ Matrix dimensions must agree.
I know I can solve this with triple integral but I want to call find_integral2 several times, i.e. , I want to again use it in another function:
F=@(y) find_integral(z-y).*find_integral2(y);answer= integral(F,-Inf,Inf);
I would appreciate if you could help me fix this error. Thank you.

Accepted Answer

Mike Hosea
Mike Hosea on 23 Sep 2013
Either this (find_integral is unchanged)
function [answer]=find_integral2(z)
F=@(y) arrayfun(@(y)find_integral(z-y).*find_integral(y),y);
answer= integral(F,-Inf,Inf);
end
or this
function [answer]=find_integral2(z)
F=@(y) find_integral(z-y).*find_integral(y);
answer= integral(F,-Inf,Inf,'ArrayValued',true);
end
  4 Comments
may
may on 27 Sep 2013
Thanks a lot for your help again. so now using 'AbsTol',1e-5,'RelTol',1e-3, I could speed up the function find_integral3(z) (mentioned above), but now I want to again use it to calculate the following integral (this is actually the final problem I want to solve)
F = @(y)find_integral3(z)(z-y).*find_integral3(y);
answer= integral(F,-Inf,Inf,'AbsTol',1e-5,'RelTol',1e-3);
Even after around 8 hours, it did not terminate! I would appreciate if you could help me again.

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