How can I use integral function this way?

function [mat_uni] = mat_unif(i,j,k,s,ro,h_b,x_b1,x_b2)

fi_jk = 2./sqrt(3).*pi.^(-1./4).*2.^(j./2).*(1-(2.^j.*x-k).^2).*exp(-(2.^j.*x-k).^2./2);

fi_is = 2./sqrt(3).*pi.^(-1./4).*2.^(i./2).*(1-(2.^i.*x-s).^2).*exp(-(2.^i.*x-s).^2./2);

mat_uni_der = @(x)  2.*ro.*h_b.*fi_jk.*fi_is;

mat_uni = integral(mat_uni_der, x_b1, x_b2);

end

The problems when integrating this function come from calling fi_jk and fi_is functions, since matlab does not recognize x as a variable that will later be used by integral().

If I delete the 'x' as an input, I am told that there are not enough input arguments. I have tried to define x using 'syms x', but other errors appeared: 'Input function must return 'double' or 'single' values. Found 'sym''.

Could it be useful to use the function handle? If so, how to use it?

Also, I would like to know what "opstruct" is used for.

Thank you very much for the possible answers.

[Jan]

What is "x" in the inputs? A vector or a symbolic variable?

[Aparicio Nieto]

It is a variable, since I want the integral function to give me a numerical value, but I do not know how to define it without having to define it as an input argument (it does not come from the main program).

Answer 1

[Walter Roberson]

function [mat_uni] = mat_unif(i,j,k,s,ro,h_b,x_b1,x_b2)

fi_jk = @(x) 2./sqrt(3).*pi.^(-1./4).*2.^(j./2).*(1-(2.^j.*x-k).^2).*exp(-(2.^j.*x-k).^2./2);

fi_is = @(x) 2./sqrt(3).*pi.^(-1./4).*2.^(i./2).*(1-(2.^i.*x-s).^2).*exp(-(2.^i.*x-s).^2./2);

mat_uni_der = @(x)  2.*ro.*h_b.*fi_jk(x).*fi_is(x);

mat_uni = integral(mat_uni_der, x_b1, x_b2);

end

Answer 2

[Roger Stafford]

I think it will work if you simply substitute those two expressions for fi_jk and fi_is, respectively, into the anonymous function mat_uni_der. It will make a very long line, but who cares about long lines? Getting it to work is what counts.

[Aparicio Nieto]

Yes! It works if I do what you say, but now I want to integrate a function that is diff(f) and writing all this stuff would be terrible. I have tried to use syms, but it has been all night working and I have not seen any result yet.

Thank you very much for your answer!

[Walter Roberson]

You could do numeric differentiation on a sampling of function values. Or you can use

syms x
dx = diff( mat_uni_der(x), x)