How to integrate between a defined and an undefined limit

Question

Trond Oesten 2015-3-16

0
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https://ww2.mathworks.cn/matlabcentral/answers/183359-how-to-integrate-between-a-defined-and-an-undefined-limit

编辑： Trond Oesten 2015-3-16

Hi,

I have performed an double integration of a function containing 3 variables. The function is now only dependent on 1 varaible. Is there an easy way I can integrate the function for this last variable to, but I want it to go between a defined value (lets say 0) and an undefined variable (a). Is there an easy way to do this? or should this be performed as a tripple integral right away? Thanks!

My script:

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];
% Double integral
fun = @(x,u,k) wblpdf(x,u,k).*reshape(mvnpdf([u(:),k(:)],mu(:).',C),size(u));
qfun_scalar = @(x)integral2(@(u,k)fun(x,u,k),ubot,utop,kbot,ktop);
uncpdf = @(x)arrayfun(qfun_scalar,x);
% Tripple integral
qfun_scalar2 = @(a)integral3(@(x,u,k)fun(x,u,k),xbot,xtop,ubot,utop,kbot,ktop);
unccdf = @(a)arrayfun(qfun_scalar2,a);