Triple integral of a function, when one of the integration limits is undefined

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Trond Oesten 2015-3-16

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https://ww2.mathworks.cn/matlabcentral/answers/183403-triple-integral-of-a-function-when-one-of-the-integration-limits-is-undefined

Hi,

I have a function with 3 variables that I want to integrate, but one of my integration limit is undefined, and I want my answer as a function of this undefined integration limit (a). I have tried using syms, but I only get that no explicit integral can be found. Is there another way to do this?

    clc; clear all; close all;
    C = [23.875 15.75281; 15.75281 93.9842];
    mu_U = 1788.2058;
    mu_K = 70.8489;
    sigma_U = sqrt(C(1,1));
    sigma_k = sqrt(C(2,2));
    ubot = mu_U-4*sigma_U;
    utop = mu_U+4*sigma_U;
    kbot = mu_K-4*sigma_k;
    ktop = mu_K+4*sigma_k;
    xbot = 0;
    xtop = @(a) a;
    mu = [mu_U;mu_K];
    syms x u k a 
    l = ((1/sqrt(((2*pi)^2)*det(C)))*exp(-0.5*transpose([u;k]-mu)*inv(C)*([u;k]-mu)));
    p = (k/u)*((x/u)^(k-1))*exp(-((x/u)^k));
    D = l*p;
    F1 = int(D,u,ubot,utop);
    F2 = int(F1,k,kbot,ktop);
    F3 = @(a) int(F2,x,xbot,xtop);