# Make an double integral function

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pankaj singh on 25 Nov 2021
Edited: VBBV on 25 Nov 2021
I want to make the double integration function (as per the formula shown in figure below) and then evaluate the integral for the given range of x and y. Please help me make the function.
My code is something like this but gives error:
fun = @(x,y) 1/sqrt(2*pi).*exp(-x.^2/2).*exp(-1/2.*(y+(u_j-u_m)/sigma_sq)).^2);
q = integral2(fun,y,Inf,-Inf,inf);

Bjorn Gustavsson on 25 Nov 2021
By putting the product inside the first pair of square brackets you've made the formula look a little bit confusing - since the only factors that depend on j and m_n are outside that parenthesized factor, but I'll give it a try...
The inner integral over x is just the error-function:
(erf(y/2^(1/2)) + 1)/2
This should give you a modified function, something like this:
fun = @(y) ((erf((2^(1/2)*y)/2) + 1))/2.*exp(-1/2*(y+(u_j-u_m)/s_n).^2);
Which for your desired values of u_j, u_m and s_n will integrate just fine from -inf to inf.
HTH

### More Answers (1)

VBBV on 25 Nov 2021
Edited: VBBV on 25 Nov 2021
u_j = 10.4;% select a value
u_m = 2.6; % give a value
sigma_sq = 1.1;% assume a value
syms x y
y = 0:0.1:10; % gvien range for y
% x = 5; % given value for x
fun1 = @(x) 1/sqrt(2*pi).*exp(-x.^2/2);
fun2 = @(y) exp(-1/2.*(y+(u_j-u_m)/sigma_sq).^2);
for i = 1:length(y)
L(i) = integral(fun1,-Inf,y(i));
K = integral(fun2,-Inf,Inf);
q(i) = L(i)*K;
end
%iwant
plot(q,'linewidth',1.5)
grid
you can try this approach ,

R2021b

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