MATLAB: Integral multiple infinite limits

multiple integral difficult infinite limits

Hi , i have to solve one more difficult integral…its an integral like this
        fun=∫[exp(-u^2)*(∫fun1(v,u,x,Kt)dv)*(∫fun2(v,u,x,Kt)dv]du
The limits are for v[1e-9,Inf] and u[-inf,inf]
I tried to transform the function mydblquad of Mike Hossea http://www.mathworks.com/matlabcentral/answers/14514-double-integral-infinite-limits but i didn't manage to do it..Is there any idea??? Thanks!!!

Best Answer

Try this:
function q = paris(fun1,fun2,x,Kt)
% q = ∫[exp(-u^2)*(∫fun1(v,u,x,Kt)dv)*(∫fun2(v,u,x,Kt)dv]du
% The limits are 1e-9 <= v < inf and -inf < u < inf.
a = 1e-9;
innerintegral = @(u) ...
  arrayfun(@(u1) ... % u1 is always a scalar here.
          exp(-u1^2) * ...
          quadgk(@(v)fun1(v,u1*ones(size(v)),x,Kt),a,inf) * ...
          quadgk(@(v)fun2(v,u1*ones(size(v)),x,Kt),a,inf), ...
      u);
q = quadgk(innerintegral,-inf,inf);
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