Matlab code that shows orthogonal functions

Is there a way to write a code in matlab to show that given functions are orthogonal? For example, I have to write a matlab code that shows f1(x)=x^3 and f2(x)=x^2+1 to be orthogonal from the indicated intervals of [-1,1].

Answer 1

[Mathieu NOE]

hi

functions are orthogonal if the integral of the product of the two function is zero on the x range (specified)

if you have to do it analytically, make the product (it's a polynomial) , write the integral of it (still a polynomial) and check the value of this integral over the x range.

this can be also checked numerically (with some rounding error) by :

x = [-1:1e-3:1];

y1 = x.^3;
y2 = x.^2+1;

prod = sum(y1.*y2);  % zero (almost)