MATLAB: How to use integral with an implicit function defined through a sum

functionintegralintegration

Suppose we have a function define as follows:
fz=@(z) exp(-(z).^2/2);
g=@(y) sum ( v(1:n/2).*fz((y- v(n/2+1:n))));
here v is a vector of length n that is known and is used to define the fucntion g.
Now I want to integrated g from [-5,5] using command
integral(@(y) g(y), -5,5).
I, however, get an error that matrix dimensions must agree.
I get where the issue is. It occurs because I defined a function through a vector and pass another vector as input.
Is there a way of fixing this?

Best Answer

By default, integral will call your function with an array and expects your function to return an array of the same size as the output. If you specify the name-value pair arguments 'ArrayValued', true in your integral call it will instead call your function with a scalar and expect an array as output.
v = 2:5;
y1 = integral(@(x) x.^v, 0, 1, 'ArrayValued', true)
y2 = integral(@(x) x.^v, 0, 1) % Throws an error
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