Nested integral and how to plot

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Orongo 2017-10-15

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Hi, I have this exercise to calculate D_x that is defined as following:

So far my program looks like this..

main.m:

% main.m
delta = 0.028559;
x=61;
mu_x=@(t) mu(t);
lx = @(x) exp(-integral(@(t) mu_x(t),0,x));
Dx = integral(@(t) exp(-delta*t)*lx(x+t)/lx(x), 0, inf,'ArrayValued', true);

mu.m

function res=mu(x)
a=0.006782872;
b=5.44781E-08;
c=0.137849468;
res = zeros(size(x));
ind = x>97;
res(~ind) = a+b*exp(c*x(~ind));
res(ind) = a+b*exp(c*97)+(x(ind)-97)*0.001;
end

There are 2 main questions I struggle with this one. 1) Is the program correct? I get a higher value then expected and I don't understand how Matlab assign integrals. 2) How to I plot the results? Say x=61:101 for mu_x, l(x) and D_x?