# Nested integral within integral2

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Juan on 23 Aug 2013
I'm attempting to take the double integral (using integral2) of a function that is defined by an integral.
Here is what I am currently attempting:
t=linspace(0,1,50);
fun_1= @(v) exp(.071*v)
fun = @(x,y) 0.14*0.00607*integral(@(u)fun_1(u),0,x).*exp(-(x-y).^2).*0.14*0.00607*integral(@(u)fun_1(u),0,x);
for i=2:length(t)
for j=i:length(t)
A(i,j)=integral2(fun,t(i-1),t(i),t(j-1),t(j));
end
end
I'm receiving the error
Error using integral (line 86) A and B must be floating point scalars.
Can anyone provide any information on how to fix this problem.

Mike Hosea on 24 Aug 2013
The problem here is that integral2 requires that the integrand accept arrays as inputs and return arrays as outputs, but integral only accepts scalars for the left- and right-hand end points. You just need to vectorize the call to integral. Also, I assume you meant to use y in the second call to integral.
n = 12; % Increase to 50 when you're ready, but be prepared for a wait!
t = linspace(0,1,n);
fun_1 = @(v) exp(.071*v);
int_fun_1_scalar_inputs_only = @(x)integral(fun_1,0,x);
int_fun_1_vectorized = @(x)arrayfun(int_fun_1_scalar_inputs_only,x);
fun = @(x,y) 0.14*0.00607*int_fun_1_vectorized(x).*exp(-(x-y).^2) ...
.*0.14*0.00607.*int_fun_1_vectorized(y);
A = zeros(n); % Preallocate A
for i=2:n
for j=i:n
A(i,j)=integral2(fun,t(i-1),t(i),t(j-1),t(j));
end
end

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